Curate, connect, and discover
So before I start I did put some though into the choices, so some of them are tied to personality, design, or simply because I think they'd like them.
I did put some self inflicted rules in.
Firstly all of they are unevolved, bar one who we'll get into.
And Secondly I have capped the number that the students can have to Three (I did do Aizawa and All Might with Four and Six Respectively, but adults and all that)
So going down the list in Dorm Order (Only List I had access to for the order)
Starting with.
Mineta
Bonsly- Mainly down to the design looking a hell of a lot like him, the short round body with the spheres on the head and a slight penchant for crying makes the little guy a pretty good pick.
Midoriya
Eevee- Seems really self explanatory little adaptable ball of floof with a big smile on it's face perfect for Izuku, and a popular pick.
Magikarp- Shiny and a gift from All Might, again a popular pick as it really is just his mindset as a Pokémon, based on the interpretation from Aresia Mark.
Deino- Seems like a bit of a weird pick but trust me it works, Deino's whole thing is constantly hurting itself trying to find it's way, sound like someone? Plus upon evolving which takes some time, it become quite potent with the multiple heads perhaps being reference to the Visages, and the fight back against Darkness? But hazy on that last one.
Aoyama
Furfou- The immediate logical pick don't think I need to explain why the fabulous French boy would have the Kalosian epitome of style, in this case he has his styled in the Light Blue Star style.
Snivy- Now this one has some ideas to it, firstly Snivy's design is meant to represent royalty specifically pulling from French, so they fit Yuga to a T, and it being a Snake would allude to his later betrayal, being a Snake.
Tokoyami
Riolu- Right out the gate we have the Protagonist Pokémon, in terms of design and lore the idea of Aura could prove an interesting contrast with Dark Shadow, plus the aloof and powerful nature of Lucario later down the line works perfectly with Fumi.
Taillow- Yep couldn't not get a bird reference here, and Taillow feels a better pick than Murcrow or Rookidee, bringing in the Samurai idea that Tokoyami has going on, plus having a flying Pokémon would help him keep up with Hawks (Who would totally have a Talonflame)
Applin- Yep this is really just in reference to his love of apples, but it could also be reference to the massive almost dragon like power held by Dark Shadow, I'd imagen that it would become a Hydrapple.
Koda
Pidove- Makes sense he uses Pigeons a lot in his tactics so this guy seemed perfect for this situation.
Rogenrola- Rocky aesthetic with the speaker look, seems super self explanatory.
Tandemaus- Again good vibes, should have gone with a Rabbit but felt that little mice would work nicely with Koda.
Jiro
Noibat- Of course we had to have the little bat on the team, as it feels better than Wismur, granted not a bad Pokémon by any means, (I used it for my playthrough of Emerald) but Noibat has the aesthetic down pat, and Noivern would be a killer ace, and it seems to be a rather popular pick for her as well.
Fenniken- Seems a bit of an odd choice but honestly I could see them playing a role similar to Serena's from XY, giving her the confidence to preform, also just a warm little guy, could be interchangeable with Scorbunny, but the Badass Magician vibe would work well with her.
Kaminari
Yamper- Yes Pikachu is a popular pick given his whole nickname, but honestly I was inspired by @birdbrainzx's choice of Yamper and Electrike, and Yamper is a better personality fit for Denki in any case.
Electrike- I feel that he would like the personality and strengths of this wolf like Pokémon, plus he could learn from it's ability to use electrical pulses to boost it's speed, having just read the Magnetic Attraction Fic the idea of Galvanic Style is still fresh in my mind so that would be pretty cool to incorporate.
Ida
Piplup- Come on, you know the little Penguin fella would try to imitate the class rep, flapping it's little flippers and trying to order the others about, plus let him have a emotional support little guy.
Varrom- You know I had to give him the engine Pokémon, that much was obvious, maybe a gift from his Brother? Honestly either could be and it would work out fine, as I like picking some with possible story telling devices.
Ojiro
Tyroge- I wanted to give him something big but I felt that a Tyroge was a good, smaller but well rounded Pokémon to give him, if I had to guess it would probably become a Hitmonlee.
Aipom- Yep, I had to, it's just right okay, he's like the one Aipom from Dogs in Love who does pull ups with his trainer, so it just felt right.
Hagekure
Helioptile- Yep Flashing lights, he also a little Lizard guy, what's not to love.
Carbink- Their a reflective diamond pretty little dude, yeah Toru's team is rather basic I think their Pokémon she likes rather than any big thematic reasons I say then picking.
Ducklett- Way out of left field with this one but it is really meant to be a sort of meta joke that being invisible she's rather well unassuming then you get the reveal that she is extraordinarily pretty, hence Swanna, also a mon that doesn't get much use so I included it here for some variety.
Shoji
Doduo- Now it was actually really hard to pick Pokémon for Shoji at first but his Pokémon are simple, like Doduo, one of his early friends back from when he lived in his Village, plus the two headed design works well with him
Shuckle- Again a simple Pokémon but one that works well with Shoji's aesthetic, a bigger Pokémon that likes helping the others, making sure they don't hurt each other too much.
Urakaka
Clafairy- Not Cleffa, now this either down to the amount of affection shown to the Pokémon when it was young so it's the most developed mon in the class, plus the space vibes and colours fit perfectly.
Meowth- This one is the Galarian, showcasing her tougher personality, still has Pay Day, but the tougher body and access to a good variety of moves and Purrserkers rage can be similar to the focus that she uses when fighting.
Kirishima
Rockruff- Of course he would have one, like Kukui, he would let his attack him, plus Eijiro just has the disposition for raising one, plus the little entry about them sensing when their trainer is down is rather cute and I think his would be rather in tune with him, totally Midnight Form when it evolves.
Bagon- He would absolutely be into the idea of Bagon's dream to fly and try to pump the little guy up at every opportunity, help them build up strength and try to fly, plus you can't deny that Red Riot pulling up on a Dragon wouldn't be awesome.
Bakugou
Cyndaquil- Again an idea from Aresia Mark, I adore the idea of this little meek Pokémon partnered with the hot tempered Katsuki, plus I like to think that they help out around the Kitchen, he also treasures that little one, being a Pokémon he caught with his Dad.
Ashido
Goomy- You can't convince me she wouldn't have this squishy little guy, a fierce little Dragon Blob that she's helping achieve the strength it dreams of.
Shellos- The West Sea form specifically, colour coordinating, would probably act like Starfires pet Silky, lazing about, but getting into wild adventures.
Yaoyorozu
Ralts- Perfect pick right of the bat the elegance and physic power would be a big plus for her, she'd show them the upmost kindness and care.
Flabebe- Blue to match the flowers in her Dorm which were picked for them, Florges is noted as for keeping gardens so I wouldn't doubt that the line would be a common sight around the grounds of the Yaoyorzu estate, and blue even more so, as they are stated to be highly valuable, and added bonus is what one will do when angered, as it's stated to fire Artillery like beams of light, so perfect for the Canon loving hero.
Sinistea- We included Applin with Fumi, so it makes sense that I'm include the troublesome teacup, perhaps it possessed a teacup in her house, and she found it so funny that they became friends, it's very particular, plus as well as the tea reference it's an object mon, so it simply works with Momo.
Sato
Teddiursa- Quite simply it loves honey, and becomes a strong beast of a Pokémon, in Ursaring, fits in with Sato just fine, as does.
Swirlix- Would I really need to explain the connection here, simply put a good choice.
Todoroki
Frigibax- Of course he'd have a pseudo legendary in his party, but it's ability is really where it's a perfect mon, as with Thermal Exchange it converts heat to energy, in this case boosting attack power, so they've been helping with the training of Shoto's firepower.
Litleo- I like the idea that whilst Shoto wasn't ready to accept his fathers power as such he didn't get the Litten that Endeavor planned to give him instead being given a Litleo, either from Rei or more likely Fuyumi, as it's more normal, with a very wild move pool, he doesn't hate the little guy, but wasn't to thrilled.
Sero
Treecko- The little lizard dude, I mean kinda a weed joke in there I guess, but I think it works, a mon that can keep up with the king of swing, plus it fits the pretty chill vibe that he brings to the table.
Sneasel- He's a little mischievous guy that matches his vibe and colours, what's more to want. Sero's are really just ones that I believe he would think are cool.
Asui
Sobble- Ha you fool you though it would be a Frookie! But no it's the sad water lizard, I think Tsu's confident nature could really help them overcome their frightened state.
Bounsweet- Not really sure but It fits her, and it's nice having a little ball of energy to contrast to Sobble.
Shinsou
Rowlet- I actually had a bit of trouble with him, but I though a little owl friend would suite him, if he was given the choice he'd pick the dapper little guy.
Elgyem- Pretty self explanatory, it messes with the opponents mind, plus again pretty dapper.
Now I would add the teams I built for Aizawa and All Might but it has taken me at least four hours to write this and I'd like to scroll this site, so leave your opinions on my choices, as I feel I got them down pretty well, maybe I'll do charts for their moves, stats and natures, but I'd have to get a bit better at drawing for that to happen.