You can get several different types of semi-automatic .22 lr rifles for around 200$ or less. Almost every time I walk into a gun shop I see one or two used ones for 100-150$, sometimes less. As everyone has already said, they're great learning/target/plinking rifles.
Ak's and the like are nice because you can buy loads of the 7.62 nato rounds (also known as the 308 winchester) on the cheap. Probably one of the cheapest rifles out their to shoot besides a .22 lr.
Otherwise, ar-style rifles (m16, m4, ar-15, etc) are also nice and fairly cheap to shoot, because of how common the 5.56 nato round (aka .223 remington). If you want to drop a large wad on one of these weapons, I highly recommend a look at les baer. They make hand built, custom matched target shooting rifles guarenteed to something like 1/2 or 1/4 moa accuracy (which is very good).
Unless you'll have some big game at the other end of your rifle, or you want to start practicing super long range marksmanship, you'll probably be well off with one of those types of rifles.