I've used hot glue, normal elmers glue, and am experimenting with elmers rubber cement.
Hot glue dries fast and strong, but doesn't give you much time to move the piece if you get it wrong, and you can burn yourself.
Elmers white glue is pretty strong, and gives you a bit of time to make sure the piece is in the right spot, but it is very slow to dry, and can start getting messy.
Elmers rubber cement is OK in strength, but you can peel the piece off with a little force, which can be good or bad, because you might mis-align a piece wrong, but then it is a little weaker. The glue also rubs off, this can also be a good or bad thing, seeing that if you get some on the ouside, you can rub it off.
Glue sticks will not work.