3) Having Characters that Inexplicably Mix Features Of Various Species With None of the Unpleasant Drawbacks you Would Expect Is Not Interesting.
(see also 'tragic life stories about being spawned in laboratories Is Not Interesting', below)
So you have a catperson with a long, presumably furry tail, big 'sexy' cat eyes, ears on top of their head and pointy teeth.
i. If their tail is furry, are they furry all over? If not, why not? Do they wax? Shave?
ii. Do their cat eyes actually look as freaky and scary as you would expect if you saw them in a standardly human face?
If not, why not? Is their face also slightly cat shaped to compensate? Does this make them therefor less appealing to the human male?
iii. Do they hunt animals, rip them to shreds and devour them in disgusting and horrible manners, in public?
If not, why not? That's what cats do, isn't it?
If you do that, do you include really gross things, like entrails and stinking guts? If not, why not? Ever seen a real rat dismembered by a cat?

3. How To Play An Interesting Furry No, having a tragic life story about being spawned in a laboratory will not make your character interesting- sorry. NO tragic life stories will EVER make your character interesting. They actually have to have interest here and now to be interesting.
I am slightly biased in this, given that I find furries somewhat disgusting and bestial, but here is my best advice:
i. see all my suggestions above.
ii. include really bizarre cat features that would not be appealing in a human, like six breasts. Like I said... imperfection is interesting. If your cat eats a whole lotta raw meat, as cats tend to, does their breath stink? It would, you know. If it doesn't, have a reason.