no gun new, is 100 bucks or less; you might find a used 22, or a mosin nagant for 100 or less. here is your problem, 5 to 10 boxes of centerfire ammo , will now cost you 100 bucks to fire. So what you need is a 22. Get a Savage 64, a marlin 80 or 81, new or used all the way back 70 years. they will be around 100 bucks, you can find other used 22's for about 100 bucks, a new mossberg plinkster will be about 100 bucks, they are hit or miss for reliability.
ammo, you can buy several diff 50 round boxes, of all kinds of diff ammo, for 2 to 4 dollars a box, and spend a lot of time, testing all diff kinds of ammo, finding out which one shoots best for you. So the 22 is the way to go for you, being that you, like myself, tend not to like to spend money.