Gonna write down impressions I have on the characters in Conquest, ranked by their usefulness (but in no particular order in the brackets except for some stand-outs). All of this has been based on my experience in Hard/Classic.
Staples:
Effie: Your workhorse through the entire early game, and manages to stay almost as relevant through everything else. Effie is a fucking boss. She's durable enough to tank nearly every early game threat and her personal skill (with her outrageous strength and weirdly high speed to boot) ensure she can dish out as much as she can take. She drops off just a bit as the game throws more ninjas and mages at you, but she's a best in class physical tank outside the royals.
Camilla: Camilla proves her worth in the very same mission that she's introduced, and never falls off. Through the early game, her pre-promote stats render her virtually unkillable short of truly insane manuevers and proves to be a vital crutch to lean on when you're caught in really bad situations - she's your delete button. Of course, she's no Jeigan either - she's a versatile tank and the fact that she's one of your few unambiguously great axe users makes her damn near essential for some maps.
Xander: It's fortunate that Xander arrives just in time for Effie to fall off a bit in terms of pure utility. Xander is pretty insane, honestly. Siegfried isn't quite the crazy weapon that Raijinto is, but it's nonetheless quite strong, and like all the royals, right out of the gate Xander is incredibly strong - strong enough that it feels a bit bad to use him at first, but he's a bastion of safety for your units from the moment he's introduced - that is, if you're careful about magic.
Elise: Elise isn't the best healer ever, but she's the best one you'll ever get. She's a fine mix of utility - her high mobility means she can cross insane distances for clutch heals, or simply to easily get out of danger zones that would be guaranteed to murder her, and her starting with Freeze makes a huge difference for saving units from being intercepted or stalling objectives. She's got an amazing Personal on top of all that - the damage reduction is crazy, especially early game, and is what really turns tanks like Effie from being very good early units to amazing ones.
Keaton: Keaton's a lot of things. But the two things that really matter about him are: a) He's adorable. b) He's an insane ball of speed, strength, and defense. He's got good starting bases and for almost everything that matters, really strong growths. He's not only a reliable physical tank (especially with Beastrune equipped), he's excellent at assassinating targets and especially tearing apart cavalry - Beastbane proves to be a lot more valuable than you might give it credit for later on. Plus, his kid owns.
Very Reasonable:
Leo: The king of reasonable units. Leo, like all the royals, is strong right out of the gate, but he's also I would consider the 'fairest' of all the royals. Even in his introductory mission, where he's at his peak relative to the rest of your army, he's not even really the best even there. He's still very good, though, and Dark Knight is an excellent class in terms of its' versatility - there's rarely a situation where using Leo is bad, even if there's not tons of situations where he's amazing either - especially since soon after you get him, the game throws tons of high resistance enemies at you. It's really his average speed that kind of makes the difference for him, though, so if you fix that, he'll go from arguably your most reliable tankbuster to easily your best one.
Niles: In a world where you didn't bother investing in Mozu, Niles is the Archer you're stuck with for a very long time - and anyways, he's still better at assassinating mages. Niles is pretty strong out of the gate, and he's almost always relevant for whatever the game chucks at you - be it locked chests or pegasus knights. He'll be able to double most things and is fast or resistant enough that it's rare to feel totally uncomfortable sending him out to do some business.
Peri: I'd love to say Peri is inarguably a staple, but I need to be a bit more clear-headed about this and say that Peri's just really damn good. Bloodthirst is an amazing Personal, a huge Rally for every single physical damage relevant stat in the game (and since Speed is so good it helps her on enemy turns on top of that with the increased Avoid) and all she needs is one kill to get the train going. She's not just an awesome character, she's an awesome unit - the best Cavalier in the game, IMO. She'll level into high strength and high speed, further cranked up by Bloodthirst which throws her damage output into overdrive. Still, she's glassier than what you'd consider ideal and while she has above-average Resistance, it's really not enough to save her from eating a lot of magic damage regardless - it might just mean the difference between being deleted on the spot or surviving the first hit for a lethal counterattack before the second. Great Knight does a good job of covering for her weaknesses, anyways, and her naturally above average Resistance means the penalty doesn't hurt nearly as much.
Jakob: Jakob is a hair away from being a pure staple. He's incredible in the early stages, but the problem is that Jakob just kinda... stops being useful the moment Felicia comes into the picture. Not because Felicia is inherently that much better, but she has the much more relevant stat for damage by that point. Still, he's invaluable for a long time, and Gentilhomme's damage reduction has a lot more value in Conquest's early game given how much you'll be relying on Effie and Fem!Corrin. His early damage output is significantly higher than Felicia's, and there's of course a lot of use you get out of his healing and debuffs. There's just... not much reason to stick with him after a certain point.
Felicia: Felicia is straight-up not very good. For a time. Kind of a long time, honestly. For all the reasons that Jakob is truly invaluable, Felicia is nearly his antithesis. With the tools you're given, her damage output is low and the trade-off in slightly improved stave value doesn't really make up for that when she's basically just budget Elise in terms of utility. Luckily, if you were benefiting from the early game edge of Jakob, Felicia comes in at the exact time she's most useful. Which is the acquisition of the Flame Shuriken. It's what enables Felicia to be so much more powerful than Jakob so immediately, and gives her an immediately defined role in the army. All of a sudden, she's the best of both worlds in being a good staff-bot while still having above-average damage.
Kaze: The other reason why Jakob just becomes significantly less useful. It's certainly true that Flame Shurikens aren't always better than the regular old kind, and while you might think that still leaves room for Jakob's stat orientation, Kaze is way more useful to have around in those situations. He's just better specialized for it, with his insane speed and skill synergy. You can use him to crack open tough physical opponents, but he's especially amazing for blowing up mages between the good match-up on the triangle and high Resistance. He has decent initial utility and he scales well, too.
Selena: I'll be honest, Selena hasn't been quite as amazing for me as she has apparently turned out for others, but being not quite as amazing still means she's pretty damn good. While not quite a Myrmidon, Selena's a potent combination of high speed and high skill, with good strength and decent defense to round out the package. She'll double most things, especially with help, and in all likelihood will wind up being one of your most reliable units for critical hits.
Azura: Pure utility, even if her inclusion always makes positioning a little more complicated than it needs to be. It's all worth it, because Sing is an incredibly powerful ability - the potential for double heals or emergency repositioning, or extending movement range, or... well, anything else, is amazing when used well and well worth the soft resets when you accidentally fuck up and give your enemy an easy vector to her because she's roughly as durable as wet paper.
Beruka: Beruka floats in the limbo that exists between a meh unit and a reasonable one, but I've had a lot of success with her so I'll stick her at the bottom of the reasonable units as opposed to the lord of the meh ones. Beruka's honestly not astounding or anything, and in terms of how you're going to use her, she's kind of just a more physically specialized version of Camilla with a Personal geared towards very solid poking and clean-up. But that's still pretty good, and her combination of high mobility, physical defense, and decent speed are really useful for some maps. Good pair-up fodder on top of that.
Meh:
Silas: He's... alright. There's not much to say about Silas, to be honest. He's just kinda alright. He's got pretty solid growths, he's useful in the early stages of the game with one-two punch of reasonable defense and good speed, but he's... well, he's not really that special, and in terms of his promotion options (which are good, but not unique to him or stuff he's uniquely better at) and how he scales, just doesn't ever really become more than consistently decent. He's a decent Cavalier with the usual promotion options and honestly, a pretty sub-par Personal. It'd be one thing if it happened while he was in a supporting position of the Avatar, but the 50% HP requirement is both too specific and... well, you're leaving your Avatar at 50% HP for kind of a lame power-up of a much less crucial unit. He's still good, just not really remarkable. Meh.
Charlotte: Charlotte is... well, she's okay. Sort of. She's not too reliable as far as hit rate goes and joins at a bit of a difficult chapter for birdfeeding. She packs a lot of heft into her axe, but isn't anywhere close as reliable as Camilla or Beruka is, and doesn't have much HP or defense to make up for it. The bonuses she gives paired up are crazy, though.
Mozu: Mozu seems attractive as a unit, but there's a fallacy a lot of people are in danger of falling into with her and characters like her - having above-average growth rates is not always the same thing as above average potential. And honestly, even adding Aptitude into the mix, Mozu's total growth rates aren't really that special. Ironically, she has a low ceiling in terms of utility and a lot of investment before you hit that ceiling somewhere in the mid-game. Conquest is a bit starved for Archers, but you really need to weigh the handful of missions in the mid-game that Mozu makes easier against the amount of XP it takes to make anything out of her before the late-game starts to render her more and more irrelevant. You can make her something else, but you really need to seriously ask yourself 'why even bother'.
Abort Abort Abort:
Nyx: When her personal is all about taking Ls and dishing them back half-way, it's not exactly a great stage setter. Nyx has the same problem that all of your early mages have, which is that she folds like wet paper to pretty much anything with a sharp end attached to it and doesn't have enough reach to hit first in a meaningful way. Her personal clearly orients her more towards being a mage-killer, but when you get her, there's really not that many mages to necessarily worry about per map, and she's so far behind by the time her Personal could possibly be even remotely relevant that like... she's just not good. Not good.
Odin: Odin's got pretty much all the same problems as Nyx, though his Personal is much more fun (and much better in general) and he's made worth it with his truly amazing kid.
Benoit: There's pretty much no worthwhile reason to use him besides his kid (who I haven't obtained) while Effie lives and breathes, and Xander is hot on her heels shortly after.
I've obviously neglected to mention a lot of other characters, but basically these are all the characters that I felt were worth saying something about. I understand that Arthur's actually not bad, and I love him as a character, but I also don't have anything especially meaningful to say about him as a unit.