A poor list of overviews for a bunch of species. Might update this one day, maybe.
(Note that these lists are subject to change.)
OFFENSIVE[]
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.
DEFENSIVE[]
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
SUPPORTIVE[]
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.
ALL-ROUNDERS[]
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.