The best character depends on the situations as I found each character to be useful in some kind of way.
In terms of the better Zombie Killer it would be Helena in her default outfit since she has the Hydra and quick shoting with the Hydra puts you on the ground which is useful since it makes it to where most attacks won't harm you and kills Bloodshots in 2 shots.
In terms of the better J'avo Killer that would be Ada in her default outfit since her Ammo Box is useful and the crossbow does a lot of damage and quick shoting any enemy with her crossbow will make any J'avo enemy be pinned on the ground (Unless it's those big J'avo that explode since that will instantly kill them, the flying J'avo because quick shoting them is a pain, and using the explosive arrows doesn't pin any enemies on the ground.).
In terms of the better All-Around character that would be Carla since she is only armed with a pistol and a grenade launcher, it's a really good combination since you'll be getting pistol ammo a lot (That's all you'll be getting in matter of fact since you don't get any grenade rounds what so ever) and it makes you want to melee more which as always gives you more time and points. Not to mention she's got the Picador which is a fast and powerful pistol.
In terms of the better combo person that would be Leon in either of his default or Pirate costume. Since he is the only character that can dual-wield it makes him the better person to do combos, and if you run out of pistol ammo then you can just use the shotgun to keep the combo going. And his Pirate outfit his assault rifle is powerful enough to kill zombies in a few shots and is useful as a melee weapon since Leon will stab enemies with the bayonett after a quick shot or a few melee hits. Also it's good to note that Leon in his default outfit starts off with a few remote bombs and this is useful in Urban Chaos as Remote Bombs can kill Woopers in one hit or can heavily damage a Supreme Wooper and open up an opportunity to cope de grace for an easy kill.
In terms of the most accurate person it would be either Piers in his default outfit or Ada in her alternate costume since they pretty much have almost the same weapons except Piers Anti-Material rifle is more powerful but has a slower firing rate and Ada's Bolt-Action Sniper is the exact opposite.
In terms of the best person for melee then it would be either Chris or Jake.