As usual, spoilers!
I'm not going to lie; I believe that the Consular story has the most coherent of starts of all of the Republic classes. Its fellow Jedi class, the Knight, feels too big for its britches on Tython whilst over on Ord Mantell you're thrown into situations which your squad should handle and rarely help out with as a Trooper or being sent all over the island and doing crazy tasks while being bored out of your mind by documentations of Flutterplume observations (which I actually would find very fascinating!) as a Smuggler. By contrast, the Consular is the "smallest"; you don't get any indication until right at the very end that you need to leave Tython. You're dealing with immediate events as they affect one small village and its champion, Nalen Raloch, but not the Jedi Order. Indeed, the most threatening things that happen that directly affect the Jedi are the theft of a holocron - which actually isn't taken that seriously at all, come to think of it - and your master
As a result of its very small focus, the story does move slowly, but given how Tython is, it suits it perfectly. The holocron theft, as I mentioned, doesn't negatively impact a village and its inhabitants by turning them all to the Dark Side - it just impacts an already-slightly-doo-lally inhabitant who already has some cult following as their champion. As a result, you're forced to be careful and be diplomatic, and this can't be a fast process in real life. Strangely, it doesn't feel like relations with the village and Twi'leks can be greatly impacted, as you only see a maximum of five unique named villagers follow Nalen. Sure, you get to defeat nameless villagers who are in your path at one point, but you can only definitively kill three of the five named villagers as a Dark side option! Whilst I do love the aspect of careful diplomacy, I do have to say that it does feel that your decisions don't hold as much weight as they seem, which of course has obvious problems.
I mentioned before that you can't feasibly see a way off Tython with what happens in this story; whilst with other prologues the obvious "you're going to Coruscant!" moment happens just before or after a fight scene and with a few more cutscenes to go, the Consular's final cutscene is literally an all-inclusive "oh no, something's happened, you're going to Coruscant!" moment. That being that
Coruscant has some absolutely fantastic moments, although you are again seeing an all-too-slow story playing out. Medicine, as diplomacy, obviously takes time, but they show Yuon to be deteriorating and going mad; the Consular spends easily up to an hour each time going out and finding the bits of information, but when they return Yuon isn't in any particularly worse state. Well, there is one time where she does fight you, but compared to what happens to others later in the story, I do feel that her turn is far too slow. Anyway, the good stuff. The Noetikons - the "JediPedia" of the Old Republic - are a fascinating concept; a nine-fold group of old Jedi Masters, including Vandar Tokare and even Bastila Shan from KOTOR, preserved their ideologies in three separate holocron-like devices (Science, Light, and Secrets) and provide answers to whomever seeks them out. Of course the three are separated and not one holds the answer, so they must be united to find the answer to unlock the secret and solve the mystery and help everybody live happily ever after.
After Yuon is cured, it is revealed that other Jedi Masters across the galaxy have fallen ill with the Dark Side plague and you and your magical cure which only you know - conveniently, the Noetikons are damaged by a Sith and aren't repaired until chapter 3 - must find and save them before calamity befalls them.
Chapter 1 is actually very interesting. As mentioned, we see these Jedi fall to the Dark Side, but what's really done well is how the different worlds on which they are stationed become putty in their crazed hands. Some, like Alderaan and Taris, are phenomenally well-done, but others, which now leaves Tatooine and Nar Shaddaa, are underwhelming.
The Jedi Master on Taris is a crazed Kaleesh. Enjoy him whilst he lasts, because he's the only non-human Jedi Master the Consular sees throughout their story. Taris is already plagued with enough problems, of course, but he goes one-step further besides helping infest Republic bases with nightmares. It turns out that he's found some major super reactor beneath the planet's surface and destroying that will destroy the planet - or, at least, have another go at doing so. The knowledge that Taris actually has a reactor beneath the surface is perplexingly fascinating; this is a planet whose superstructures have been blown wide open, and yet somehow there's this reactor which still functions and serves as a fundamental power source? How on earth is that thing maintained? Regardless, it's genuinely worrisome and, working well with the atmosphere of the planet, tense and disturbing.
The Jedi Master on Nar Shaddaa seems more interested in gaining more technology for his followers and overthrowing the Hutt Cartel. Something many would agree with him on even without his ability to control people's minds (which can be negated through technology... somehow...). After trying and nearly succeeding in destroying an entire planet, this seems much less impressive and actually sort of justifiable. Tatooine's Master tries to unite the Sand People, claiming them to be the ultimate warriors. There really isn't much else to say.
Alderaan, though, is fantastic. It takes the Consular back to the more diplomatic roots of Tython. How? By having you protect a noble House, defeat the champion of another House, and then become the Emissary of the first House for a Summit on a summit which is negotiating peace talks. All this while a Jedi is overseeing the talks but secretly desires to turn the houses onto each other and cause open warfare. Whilst nowhere near as impressive as destroying a super reactor, I can pontificate for pages on why I love this idea. To summarise, though, the idea that destruction of a planet can come not from external sources but from internal affairs is an amazing message to carry across whilst putting it next to the whole Dark Side plague factor.
Something which may have become apparent is that no discernable "Bad guy" has been mentioned. This is because he is the only actual villain to have major build-up and very few appearances. Compared to so many other characters who could be and are villains, we get so many who are "obviously" the bad guy after the prologue, Balmorra, and the conclusion to chapter 2 that to have someone who is only referred to, not even by name, and not even knowingly directly, for so many times until his actual appearance is so very refreshing. From the prologue and throughout chapter one we hear "Parkanas" mentioned. In the intermission between Nar Shaddaa and Tatooine we hear "Lord Vivicar" mentioned. As soon as you realise that each Master mentions Parkanas (you even get to say "Parkanas again" on Alderaan!) and that Sith Lords were known not to take their own names, you realise that Parkanas is Lord Vivicar and that he's out for revenge. Staple stuff, but remember, this realisation becomes apparent half way through chapter 1 and your character doesn't even voice it until you're about to go face him. It's big and it's exciting to finally have this revelation pay off, and it actually does pay off. You either free Parkanas or kill him, although killing him also kills every Jedi he's ever touched and spread the disease to. Fantastic wrestling of judgement here.
Chapter 2 of the Consular takes Tython and Alderaan's diplomatic influences and writes itself purely around diplomacy. Whilst you become the fastest-promoted Jedi Master in history and earn Hayden Christensen's ire, you're forever tethered by the Supreme Chancellor and Jedi Councillor Syo Bakarn to a group of politicians whose planets are threatening to secede from the Republic. That said, Balmorra's seems sort of neutral, and Sarkhai has sent two representatives who seem to want to stay with the Republic and do nothing to further the interests of this Rift Alliance. Otherwise, the other representatives, Diab Duin, Blaesus, Shuuru, and the spawn of Jabba known as Alauni, want the Jedi to do everything to help their worlds and interests. The problem here is that the planets they represent are Aeten II, Erigorm, Manaan, and Saleucami, none of which are locations which can be visited at any point in the Consular story. Instead, outside of Balmorra actually being a location, we get to help their assets on other worlds, such as a Selkath facility on bloody Quesh and some military initiative on Hoth. It really doesn't do much to cement how crucial these worlds are if we never see why.
Anyway. The Consular's interactions on Balmorra basically entail freeing the captive President and electing the Alliance's representative in his place. Considering that Balmorra is, as I said, the most prominent of all worlds represented simply because you can visit it as part of the story, I do think it's a shame I can't find much more to say than that which relates to the story. You do meet interesting characters, such as Zenith, and even get to kill one of the best Imperial NPCs out there, Darth Lachris. Otherwise, no, nothing. Hoth is only really interesting because of the strange concept of a suit of armour having healing powers. Implants, I can see, but armour that can simply be worn? Not likely, but it does make for an interesting villain.
Speaking of interesting villains: this time, we actually get a face and a name quite early on. I can't remember his name (goes to show how effective he was), but you are at least contacted by a Sith Lord whilst on Quesh. He reveals that he knows what is going on on-board your ship with the delegates, indicating that there may be a traitor among them. This is then forgotten about until the very conclusion of chapter 2, and it's revealed that one of the delegates - Blaesus - has been a Sith all this time. After the slow and drawn-out reveal that belonged to Lord Vivicar, this does feel very forced. You don't even suspect Blaesus because he's quiet and meek but others, notably Shuuru and (good lord) Alauni, are loud and pushy and much more "obvious". Indeed, Blaesus himself becomes loud and pushy when in his Sith persona! However, he's easily dealt with, and it becomes apparent that there are others just like him: The Children of the Emperor, hidden by the mysterious "First Son" who is obviously going to be the chapter 3 boss.
War finally breaks out and the Consular is tasked by Syo Bakarn with showing the Rift Alliance what the Republic can do in times of war by raising an army which is in absolutely no way officially sanctioned by the Republic and is composed of a two vastly-different alien species who otherwise are kept to their worlds. I'm not exactly seeing where the Republic ties into all this...
These worlds are Belsavis and Voss, and the armies belong to the Eshk-kha and the Voss. Yes, the first army belongs to a species that went mad and had ideas about enslaving the galaxy, and is now being forced back into their tombs and being slaughtered by the Republic. I really can't see why the Republic would ever dare sanction this, but everyone - including Alauni - rolls with it. Sadly, apart from meeting a living Rakata, the story of Belsavis is unfortunately very bland. The idea that someb members of a species that tried to enslave the galaxy believe that their fellows were wrong and tried to stop them would be especially interesting, but it isn't given the focus nor the time which it deserves in order to make it so. It probably doesn't help that they made the Emperor's Child perhaps the least human-looking human possible. He also really needs to work on his make-up, because his eye-liner is not regulation.
Voss, thankfully, is much more fascinating. If you know anything about the Voss, you'll understand why the concept of taking a platoon of them away for your own ends is very, very important. In fact, you not only take a bunch of their soldiers away, but you actually help one of their number fully-develop his skills as a Mystic and then take him away, too! You also get to see a healing ritual. A great deal about the Voss culture is learnt by seeing all of this and you learn exactly what sort of weight Mystics hold in this world, the pains they have to go through, and the prestige offered to them at the end. What most other classes see are the Trials in the Shrine of Healing and Bas-ton's tea house. Nothing really awe-inspiring, particularly as Bas-ton doesn't offer Earl Gray and has an over-abundance of Tetley's. The Child of the Emperor here is handled much better, as instead of being "evil-evil-evil" from the off as Mr. "Make-up" was, she is instead the helpful individual who points you to your Mystic and then disappears until the end where she meets you on the space station. Subtle and very welcome after Belsavis.
So after these are done, you go to Corellia and learn the identity of the First Son: Syo Bakarn, who had been helping you since chapter 2. Reminder here that Bakarn is a member of the Jedi Council, yet the First Son decides to go to Corellia and wreak havoc rather than have a group of hidden Children on Tython and destroy the Order from the inside. The idea of a Sith whose identity is hidden from whomever he chooses - even his light persona! - is horrifically underused in the name of finishing the story. Anyway. You use your forces to disrupt Imperial operations and wend your way towards his base, which curiously is a rocky cave beneath a building. Reminder: we're on Corellia. I don't think rocky caves beneath a building can easily exist on a city-planet, but at least it's not your typical boss fight in a city location.
Depending on your decision at this point, the outcome of your character's conclusion does change. Killing Bakarn and going Dark will result in you becoming the Council's combat advisor, whilst sparing him and going Light will result in you being elected to the Council itself in his stead. Quite how they manage the Council void in the Dark option is unknown, but there is at least a "chief combat advisor" present for both outcomes in the form of Master Oric Traless. The circumstances of the conclusion, of course, don't change; you will regardless be rewarded in a ceremony on Coruscant and get the chance to name a permanent representative from the Rift Alliance to the Senate: Shuuru, Diab Duin, or Alauni.
The Consular story does have a lot of fantastic moments. Tython, Taris, Alderaan, and Voss are all handled superbly, as is the reveal of the chapter 1 boss, and whilst everything else isn't bad, it is definitely vastly underwhelming in comparison. I mentioned earlier that I'd seen both full-Dark and full-Light for this, and I must admit that this disparity has been interesting; Dark is more fun and bold, but Light is easily the closest we get to learning what it is to be a Jedi in the base game. Compare this to the Knight, who only gets one mission to this effect and even then it's present in Shadow of Revan.
Is it the weakest overall, then? The Consular story presents great themes and ideas, but they are mixed in with mediocre executions and lost opportunities. It also doesn't help that the Consular story does move slowly throughout, which works well for Tython, Voss, and Alderaan but doesn't synthesise well with the majority of other planets and situations out there. I do have to say I consider the wasted opportunities of the Smuggler to be more infuriating, but as I will go on to discuss, all classes have moments which aren't executed well. I don't want to say which I believe to be the weakest of all stories at this point, but I do admit that there perhaps should have been more to this story than there actually was.