A character's personality matters a lot to me. His/her fighting style is secondary to me.
The first and foremost criterion for me is: do I like his/her personality and/or can I relate to him/her? I have to love the character, and that's where you start. That's when you start to practise combos at a more serious level (though I can't say I practise seriously and/or frequently. I confess nowadays I am not really playing CT as seriously as I appear to sound). Even though you might be fit for one character's fighting style, if you don't like/love that character I think you are less than inclined to practise that character. That's my philosophy.
Personality-wise, I should say my favourite (amongst playable characters) in CT is Rachel, probably followed by Jin. Rachel might look arrogant and high-nosed at first, but I think she actually cares (one of the alternate story paths in CT, where she shows the "dere" part of her tsundere) about Ragna, and perhaps the world. Oh yes, I love black tea too. In CS (if a PC version gets released, I hope!), I am considering Hazama and Rachel. Rachel for the same reason, and Hazama is just like Joker. Cynical, mad, twisted, intelligent. A guy who actually knows what he's doing. Put outstanding voice acting by Yuichi Nakamura on top of that, and he's just perfect. Design-wise I find the three aforementioned characters quite satisfying.
Other characters within my interests include Nu/Lambda and Hakumen, but I don't think I will get to them until I solidify my mains, which will probably take a while.
Based on what I have read I am starting off with an advanced character, but hey, I like Rachel. I am going for it.