Can I use oil and acrylic paint on paper, or do I need actual canvas?

I’m trying to get into painting. I like to sketch, but my aunt is a great painter, and she just gave me a bunch of supplies so I can get started. I have a notebook full of thickish construction paper. I also have oil and acrylic paint: Can I use either or both on this paper, or do I need canvas? How much does the canvas cost? (And while you’re at it, would you mind briefly explaining the differences between oil and acrylic paint?)