Is fin. Is board. Is lift ... duoh
Hang on. I think I misread your query. You want to know how different fin configurations affect board performance?
OK I'll start.
To start with fins are foils and they follow the same rules as air foils. Hydrodynamics and aerodynamics are the same as far as foils are concerned, just scale differently. There is specific info on the web about foils sections. Google NACCA.
Long span and short chord = most efficient for lift/drag so if speed is the priority then long fins rule.
Short span is better for manoeuvrability. There is some doubt as to whether the traditional curvy wave fins are an optimal configuration, but short is definitely better.
As I understand it fin tips produce induced drag so minimising fin tips is better for efficiency. That's a can of worms that has yet to be exercised. I'm waiting for someone to make a quad fin speed board to sail in very shallow water so we can see what happens.

Generally multifin configurations are going to be draggy so they are limited to wave boards. They could be use for freestyle I guess.
Thickness I think is proportional to drag (not sure) but thin fins definitely have less drag. Thickness is qualified by structural requirement and flex. There is a wide variety in fin stiffness these days. Its particularly important in long span fins. I understand even tiny little freestyle fins need a bit of flex.