I'd agree with Sue that thinner papers work well, they are easier to cut, but at the end of the day, I use whatever patterned scraps I can find that work with my design ;-). And I use a liquid glue, my personal favourite is Aleene's Tacky, or a glue pen sometimes for very small pieces.
We have a great tutorial for 3D paper piecing, too:
3D Paper Piecing Tutorial - Splitcoaststampers. I've bought the glue she uses, but I still haven't actually tried it out yet.