Most characters in Skullgirls are very different, so there's a lot to choose from.
Filia is a very aerial rushdown, with a big focus on cross-ups and resets.
Cerebella is the one of the two grapplers of the game, and has quite a few command grabs. She's pretty beginner-friendly at lower levels.
Peacock is full-on zoning, with plenty of projectiles.
Ms. Fortune has two playstyles; with her head on, she's fairly straightfoward and plays as a rushdown, while without her head she's basically the puppet, or the Carl, of Skullgirls. Without knowing much about either of those things, you've got a main character and another entity on the stage you need to micromanage. She's considered one of the three hardest characters to learn.
Parasoul is either played as a zoner or a rushdown, whichever you prefer with her moves and specials. She's got a few projectiles, but also has high damage if you play offensively, along with plenty of mix-ups.
Painwheel is a rushdown, focusing around flight canceling into her air normals. Her combos are difficult because of this, along with her playstyle being weird, so she's another one of the three most difficult characters.
Squigly is a stance-canceling mix-up character. You need to charge up one of her stances, and with a charge you can cancel her moves. She's very combo heavy, and her neutral/pressure is odd, so she's the last in the three most widely-excepted hard characters.
Valentine is another reset-heavy rushdown, with a few projectiles. She's not really basic or easy, but straightfoward, much like Filia.
Double is good at everything, so it's up to you how to play her. She can zone, if you prefer that, but she can also play as a rushdown if you prefer playing offensively.
Big Band is large and slow, while also being a rushdown. He's not a grappler, just slow.
Fukua is probably, in my opinion, the simplest character in the cast. She's got projectiles but is actually pretty offensive. She's considered the best character for beginners.
Eliza is just..weird. She's got long combos and is very pressure heavy.
Beowulf is a grappler, but a weird one. Instead of having multiple command grabs, he has his main grab but has many options off of it. He also has a chair mechanic where he has different heavy normals and some specials without his chair. He's really interesting.
Robo-Fortune is also a zoner, more than Fukua or Parasoul. She's got a lot of good projectile options and she has a double-jump used in her combos often.