A poor list of overviews for a bunch of species. Might update this one day, maybe.
(Note that these lists are subject to change.)
Note that not all of them are powerhouses. Some of them just do nothing but throw themselves at you.
Atomic Boo: Big, beefy immobilization machine.
Blooper: Poison, and then destroy.
Bob-omb: It's a bomb. What do bombs do? They explode. What do explosions do? They hurt. Everyone.
Boomerang Bro: The king of AoE. Hold the POW buffs.
Broozer: Punch, and then get pissed. Repeat.
Bullet Bill: Can deal 6 damage to you before the battle even starts. Oh, yes.
Bzzap!: Free -8 moves. Two turn knockouts are almost inevitable.
Cherbil: Safe debuffs. No RNG, impossible to fully avoid. No catches.
Clubba: A meat shield with a dangerous, spiked club. Notorious for being a landlubber.
Craw: Make the battle as boring as possible. Maybe they'll forfeit before you kill them.
Fire Bro: The burn never ends.
Fly Guy: Splash damage attacks out the wazoo.
Fuzzy: Steals every single stat you have except BP. Just envision the pain.
Goomba: With the right setup, it can kill you in one hit! That is, if you let it setup.
Growmeba: Ramp up attacks after each turn and deal some sick damage.
Gulpit: Immobilize your foes, freeze your foes, quake your foes, spit rocks at your foes. Just be a general douche.
Hammer Bro: B A R R A G E.
Hurt Plant: The people you can't soften, you can poison.
Ice Bro: EVERYTHING IS FROZEN. THERE IS NO ESCAPE.
Jabbi: SPAM THE STATUS EFFECTS GO GO GO GO.
Lava Bubble: Fire damage. Fire damage everywhere.
M. Bush: OH THE POISON PLEASE MAKE IT STOP AAAAAAAAAAAA
Magiblot: A wacky trickster that fakes you out with supreme bullshit.
Monty Mole: Can flip this, can flip that, and can hit you when you can't hit it.
Mr. Blizzard: Freezing + AoE = EEEEEEEEE.
Muth: MAXIMUM POWEEEEEEEEEEEEEEEEEEEER!!!!! (((((minimum speed)))))
Nibbles: Bite them, and then spit water on them.
Pianta: Fuck 'em and chuck 'em.
Pider: Enjoy your 0 SPD you cluck.
Piranha Plant: Cue the vine'd compilation.
Pokey: Poisoned here, soft there, cursed everywhere. And for good measure, let's make you unable to attack as well.
Ptooie: A Piranha Plant with legs. Gotta go faster.
Pyro Guy: Hurt yourself to do more damage. Recommended for real life.
Raven: Become Angry Raven, destroyer of worlds.
Ruff Puff: Defense is futile. Immobilization is inevitable. Two strikes, and you're out.
Screamy: Pierces defense without elements. Does a lot of things, in general.
Skellobit: Never-ending freezer. Can put your plans on hold, and put you in sticky situations.
Skellobomber: Never-ending summoner of never-ending minions. A flying Skellobit / Dry Bones.
Sledge Bro: Buff your POW so you can do repeated -8s with your 12 HP.
Slurp Guy: Y O U R S T A T U S E F F E C T S A R E M I N E .
Snifit: If not blocked, a force to be reckoned with. If blocked? Eeeeeeeeeeeehhhhhhhhh...
Snow Spike: An AoE, freezing Clubba. aiifdugdfiopgfdajgfdl
Spear Guy: Disables your FP, disables your items, and can still deliver a mean hit.
Spike: A Clubba, but without every downside (and upside) a Clubba has.
Spiked Goomba: Don't even consider aerial attacks. Like, even against anyone else. Taunt is a horrible thing.
Spinia: The only time you don't want to have flight.
Spy Guy: Given time, it can permanently remove your attacks. You can't attack with attacks you don't know.
Swooper: The less offensive cousin of Fuzzy. Steals BP, traits and moves from the enemy.
Wiggler: Gets stronger the more it's hit. AoE beware.
Wizzerd: Tear up the battle field. Hear the words "Not Enough FP" many, many times.
X-Naut: RNG beckons my child. Random.org wants to come back.
Yoshi: Everyone shall do half damage forever.
Zombie Shroom: Become a walking behemoth of disease and spread the infection.
Can protect their team from a lot of harm, and take a serious beating before falling. They can also deal a ton of damage. That being said, they rely on one strategy and one strategy alone. Break it, and it's over.
Blobule: Cannot attack, but still manages to be absolutely annoying.
Bone Goomba: Let the Hyper Charge combos loop forever. We all wanted this.
Bony Beetle: It never stops coming back. And yes, it still has bombshell.
Bristle: Flipping it does next to nothing, you can't ram it, you can't jump on it. Ughhhhh.
Buzzy Beetle: Takes 0 damage from you, deals 1 damage to itself to deal 4 damage to you. Flip it or die.
Cleft: Because taking 0 damage and redirecting it to the enemy is absolutely fair.
Dry Bones: Completely unkillable. A huge time waster, or an infinite threat.
Floro Cragnien: Has a ton of HP, but bad moves. Use badges or friends to turn into a horrible monster.
Fishbone: When ruining status effects once just isn't enough.
Hooligon: Starts the battle completely invincible.
Koopa Troopa: If you don't flip it, you are in for one shell of a ride.
Mister I: Stop your enemies from attacking in an odd assortment of ways.
Parabuzzy: A flying Buzzy Beetle, or whatever.
Paratroopa: If it ain't grounded, you're going to die. If it ain't flipped, it ain't going to die.
Shield Guy: R.I.P. any Hammer Bro, Lakitus, Magikoopas, Spikes, etc.
Shlurp: The defense king. You can't get more invulnerable than this.
Spike Top: Sacrifice a bunch of health for a spike. I hope you weren't planning on jump flipping.
Spiky Parabuzzy: Can't be jumped on, can't be quaked. It's projectiles or nothing.
Spiny: Mega Charge, destroy. This time, flipping isn't an option.
Whomp: Shield your entire team from attacks.
Yux: Defense: 0%. INVINCIBILITY: 100% OH YEEEEEAH
Helps team mates by buffing them up to the extreme, but in most cases, cannot hold down battles themselves.
(basically if you are a loser without friends don't pick these)
Barribad: Buffing your entire team all at once! GOD HAVE MERCY
Blue Magikoopa: The all-rounder of the supportive class.
Bub-ulb: Balls to the wall support. It's the only thing it can do.
Crazee Dayzee: SLEEP LOCK LET'S GO.
Cursya: The anti-support, but still support. Has some deadly curses, but requires the help of others to use the curses right.
Floro Sapien: No buffs, just tons of defense removing mayhem.
Foton: Get status effects that increase in power after each turn.
Gray Magikoopa: You can't hit what you can't see.
Green Magikoopa: Raises defense, pierces yours. Life is unfair.
Longator: Double or half POW at your own will, and then destroy.
Medi Guy: Healer by day, healer by night. Expect the expected, and nothing more.
Nimbi: Strictly curing. Healing over, and over, and over, and over.
Puni: Double the buffs. Double the fun.
Red Magikoopa: The most offensive supportive class. The attack buffs go flying.
Sombrero Guy: Buff stats to the max, and then crush a skull with a guitar.
Tileoid: Get all souped up for one glorious turn.
Warpid: Gotta go fast, you're too slow. Make your attackers double the trouble.
White Magikoopa: Heals their allies, removes the buffs of the enemy. More offensive than Medi Guy.
Yellow Magikoopa: Electrify your allies... and your enemies. Zappin' to the extreme.
Good at everything, excel at nothing. Weaknesses are specific; no hard counter.
Ackpow: Every stat increase comes with a price. And also a scar or two.
Bandit: Depending on what items or badge it steals, it can be any of the above, or none of the above.
Big Sammer Guy: Unpredictable muscle of doom.
Boo: You can't move. You can't hit me. You can't use items. You can't use that move in particular.
Boomboxer: POW boost to the extreme. Like, the biggest extremes. You can't get better.
Bulky Bob-omb: Charge the perfect Super Mega Hyper Ultra KABOOM Supreme Ultimate Deluxe 2: DX: Battle: 2: Collectors Edition.
Bumpty: Put the enemies on ice (xdd) and use the unholy power of Payback.
Chain Chomp: Has defense, hits hard, and can fully heal itself in the span of 1 turn.
Cheep Cheep: Remove all status effects now, and forever. R.I.P. fire species.
Choppa: Situational, but very effective when successful.
Crumpled Boo: It's all-rounded in it's uselessness.
Dino Rhino: The perfect distraction.
Doogan: Your moves are his, whether you like it or not.
Duplighost: Can be ANYTHING. A N Y T H I N G.
Groove Guy: While he cannot support directly, his status effects prevent both him and his allies from being hit. Ever.
Jawbus: An offensive species with a specific defensive advantage and disadvantage. Worth it, or not worth it?
Jellien: A weird assortment of attacks. You'll never know what to expect until it happens.
Koopa Striker: A defensive Boomerang Bro that comes with some risks and rewards.
Lakitu: Maximum vanilla.
Lil' Sparky: Electric attacks to the max.
Ninji: Does ninja stuff. You know the ones.
Ninjoe: The fastest all-rounder in the west. Yes, a western ninja.
Paragoomba: If you have defense you can probably just give up now. If you have only ground attacks you can probably just give up now.
Sammer Guy: Unpredictable to the max. 46 moves seems fair.
Security Guard: Taunt 'em, increase defense. Insert crying face here.
Shayde: As long as you have a team mate with you, you will never die. Ever.
Shy Guy: The definition of an all-rounder. It can do anything! But there's no winning strategy here.
Small Sammer Guy: DOUBLE unpredictable. Oh the humanity.
Sproing-Oing: Attack beyond the grave, but in groups of three!
Squiglet: Go into warp speed velocity and do some wacky hijinks to those who are less fortunate.
Star Kid: The species with 8 SP moves. You know the one. Classic.
Thwomp: Deliver instant kills on a 2 DEF plate.
Toad: Badges or nothing, baby.
Urchin: Protects you from those pesky physical attackers, among other things.