Sure, lots of people crumple up newspaper into appropriate shapes, and  tape them with masking tape (usually).  Then you can attach the shapes together, either with glue (sticking part to part), or continue with the masking tape.  When you've got the basic shape right, then you start applying strips of paper that you've brushed glue onto (usually one side) and overlap them, first in one direction, then in another.  For smaller additions, use smaller crumpled balls (like for the muzzle of a dog) on top of the paper strips.

You can use nearly any kind of paper you want; all the kinds you mentioned are fine.

I don't quite get the rings... are they glued together to form like a skeleton, then the strips are pasted over them?  Or are they a decorative shape by themselves?

I've never used nail polish for the final coat, but I don't see why it wouldn't work.  Just make sure that your whole project is dry before you try to coat it with anything; any moisture will turn into mold and ruin your piece.

Sue