birdshot: (size 9 is tiny, size 5 is medium, size BB is big). These are for small game and birds.
buckshot: (#4Buck is smallest (.24 cal) and 000 is biggest (.36 cal)). These are for larger game and defense loads).
slugs: (two varieties: Rifled slugs are for smooth-bore barrels and are big, fat hunks of lead. Sabot slugs are smaller bullets encased in a plastic sleeve...these are normally intended for rifled shotgun barrels or barrels with a rifled choke.) Slugs are for shooting through barriers and for hunting medium/large game at a distance.
As far as shooting paper, use any of the above three. The dispersal of pellets you see in the paper is called the "pattern" of the shot. Use the pattern to determine the effective range of your shotgun/shotshell combination.