Who's the best?
As of NSC 2.11 the balance is generally considered good enough that you can play whoever. Ray and Kudlak are generally agreed to be the best, and Cait & Sith are generally agreed to be the worst, but anyone can win.
Who Should I play?
No character in chaos code is really so hard to play that you should avoid them, so feel free to pick whoever you like for whatever reason. If you want a brief rundown of how characters play:
Kai - A shoto-esc moveset with oppressive air-normals
Cerb - Good footsies and unique meter management with his bullet gauge
Celia - Unique dash types, delayed projectiles, and good meterless damage
Rui - Simple but strong moveset with a focus on close range pressure and mix-ups
Kagari - Good fireballs and a good DP with solid reset options
Bravo - Grappler with a surprisingly well rounded set of tools
Hikaru - Shoto-style character who gets very high reward off of counterhits
MG - Strong pressure and mix-up with high stun damage and good reset potential
Ray - Unique stance pressure which gives him very high damage and unique command dodges
Vein - Big normals and really active fireballs help him limit his opponent's options
Kudlak - Snipes specific spots on screen, can summon zombies to slowly approach
Cthylla - Oppressive lockdown with high reward on hit
Hermes - Trap based zoning and setplay
Lupinus - Good mobility and wallcling is an extremely strong mix-up
Cait & Sith - Puppet character with lots of opportunities for setplay and strong high/lows
Catherine - Good normals and corner carry with strong okizeme setups