For $200, you're pretty much stuck in shotgun territory, but you can probably find a used Rossi single shot in your caliber of choice for $200 or under. Maybe... Maybe a single shot H&R might fall into that price range, but they are generally a little higher, at least from where I'm at. $225-$250, bottom end on an H&R.
For a little more, I'd recommend a Savage Axis or Ruger American. I owned an Axis in .30-06, and while I didn't care for it much, it would certainly get the job done. Available in many caliber options. I have no first hand experience with the Ruger, so can't honestly comment one way or the other. I just know they are the budget rifle in the low end of the price spectrum.
Ignore the comments like
$200. won't even buy a decent pile of ammo let alone a quality gun.
for they are spoken out of ignorance or elitism. Same sort of though process that knocks on Hi Point pistols, which to me, yields an attitude of 'better unarmed than unfashionable'. But that's another topic.
$200 won't get you an heirloom quality gun that will be cherished by your thrice great grandchildren, but it'll put meat on the table for a good many years. My Maverick 88 is my go to shotgun, bought new for $159.00. It has put meat on the table, and brought many hours of enjoyment.