A lot depends on what kind of face you have. However, Always avoid layering in such kind of hair because layering adds volume and you certainly don't need that with thick and curly hair. I would suggest a short bob. Avoid blunt ends as that would make you look like a pyramid. Ask for soft, textured layers only around your face.
I have very thick wavy hair and got my hair cut into a bob that falls right below my chin. Since I have so much hair I got it texturized (thinned) as well. I have a round face so I didn't want it to fall right at my chin as that would have made it look rounder. Its a great cut because I can part it on the side or in the center, pull it halfway up with a clip, secure the side with a barrette, and blowdry it straight.
Chin length bob... Go for it!!!!!
Depends on the SHAPE of your face.. And how it would suit you...