You will love the right pellet gun. Search for the break opens ... look for something that will be in the range of 1500 fps. I've actually killed raccoons with mine. I had to keep peppering that bastid, until it finally gave me a decent head shot. Dropped from the tree like a rock. Not a small one, but not huge ... around fourteen pounds. Last year I trapped one that weighed in at thirty-six pounds.
The lowest price, that hits that bar, I believe to be a Gamo. I have one and it ain't the best ... However, for the cost ... a really good buy. Lousy 4X scope, but it's enough to have fun ... and, you're not competition shooting or going on a safari ... so, it's definitely good enough. I believe that a decent model, .177, can be had for under a hunnert 'n a half.
Alloy is best, but you'll break the sound barrier and some neighbors might think you've discharged a firearm. So, just use the lead pellets .. They're enough to drop a raccoon. Moreover, dirt cheap .. less than two cents per round.
You'll have a (hopefully) legal blast.