Personally, I can go for anthro or feral - I like a design that can be recreated without too much headache, but nothing TOO basic. I like cool tones, bright colors, rainbow, etc. if clothes or accessories are included, I prefer them drawn to the side or an alternate naked form be available - If the clothing is too large, it covers too much of their markings. Species, I'm a bit flexible on. I like fluffy or scaley things, ponies, etc. 

Style can vary; so long as the character design can be deciphered and recreated from the adopt. Facial expression has little bearing on my adopts. I do tend to go for something that has a "cute" factor, either in the design or the lineart, but it's not a hard and fast rule.