I have very fine, thin curly hair. What style & cut would work best for this?
Layers, definitely! They add body to fine hair and allow curls to spring up and be well-defined. Carefully-cut layers made a huge difference to my 2b/3a hair in terms of weight and definition. Just make sure that they're not too short-shoulder length is a good standard to go by.
I would go for a shoulder length cut with layers. Cutting your hair shorter will take off some weight adding some volume.