IMO the first thing you have to do is pick your cartridge and ammo. Personally I would go with a 22 LR, and I would choose sub-sonic rounds. These rounds are more than powerful enough to kill or to bark squirrels. A 17 HMR or 22 magnum is irresponsible in the squirrel woods. Way too much power, and way too much down range performance. Choose the slowest sub-sonic that shoots well in your 22.

When shooting sub-sonic's alot of them will not function a semi-auto rifle. So I do not believe a semi is a good choice.

That leaves us with lever actions and bolt actions. If you really like the faster action then go with a 9422 or a Marlin lever. That will push your budget. But they are the best. You can get a Henry in your price range, and alot of people like them. But personally the receivers and the plastic turn me off.

The next choice is a good accurate bolt action. I would look for a good used Remington bolt action 22 like a Remington 581. Or some of the other bolt actions that Remington made.

I would skip the Savage's and the Marlin's, but that is just my opinion. You have enough money to buy a really nice rifle so find that good used Remington 581 and you will have a fine rifle for life.

Then a scope. A simple scope is all that is need. I shoot alot of squirrels with open sighted rifles.

A 2X7 is more than enough power. But personally I would spend my money on a higher quality fixed 4X scope.

I see guys all the time with 3 or 4 or 5 or 6 different 22 LR's. I never understod that. I would spend my money on one top quality rifle before I would own that many different low end quality rifles. Just an opinion. Tom.