If you can find a 10/22 under $200, go for it.
great rifle for learning marksmanship, and a lot of cheap fun for plinking.
Last i saw, marlin model 60 rifles were pushing the $200 mark, and while that's what i started out learning to shoot with, the
Ruger is IMHO a better tool in the long run.
maverick or Remmy 870 express are both good shotguns.
buy used if you can find one - should be able to get one well under $200.
not knowing how big you are, I'm going to suggest a 20 gauge to start. lighter recoil, lighter overall, so faster to come on target and faster for the followup shot once you have some practice under your belt. (a lot of cowboy action shooters prefer 20 gauge over 12 for these 2 reasons - and it's still a good home defense round)
which one to start with depends on what you want to do.
plink, target shoot, maybe pot the occasional rabbit or tree rat? 10/22.
bird or deer? shotgun. (you can hunt deer with rifled slugs)
either way, good luck and let us know what you get!