Working the action on your new shotty wll loosen it up, so lube it and cycle it repeatedly. Don't worry, you won't go blind.
For or clays and such #8 shot is what I use.
Shot is kind of like copper wire, the bib bear the number the smaller the shot is in diameter.
Small shot for smaller targets at closer range. Heavier shot for larger targets, thicker skin/hide and longer distance.
#8 is smaller in diameter than #4, but #8 has more individual shot per shell.
#9 through #6 for dove, quail, grouse, etc
#6 through #4 for squirrel, pheasant, turkey, etc.
Shot larger than #4 is usually in the waterfowl category, thick feathers and longer shots.
However, 000 buckshot is larger in diameter than 00. The only sizes of buckshotI have encountered are/were 000, 00, 0 and #4. 00 is my preferred combination of size and quantity per shell.
For HD scenarios, I like the Winchester military grade 00, it is not terribly expensive and will not separate your shoulder when you shoot it through your pump gun at the range. Putting 3.5 inch rounds through a pump shotgun is a form of self flagelletion I can live without.
Some of the information above is my personal experience and the results of others may vary, aka YMMV.
Fet to a range or clays course and enjoy your new shotgun.