I play some classical, and although I believe the purists answer may be that you only use 3 fingers + thumb, I use them all when necessary. I can't see any reason not to. I've passed grading exams using all 4 fingers, so it can't be that frowned upon.

I'd suggest looking at some classical pieces, as they're all finger picked. Maybe also beatles stuff? I remember learning blackbird years ago - nice tune as well....