Th e Henrys are cool and fun and cheap. Perfectly suitable for squirrels at 25-50 yards.
A bolt gun is a good choice if you are into accuracy. I like CZ. The Ruger 1022 can be an accurate SOB if you put some money into it. Marlin and Savage make inexpensive .22 that shoot almost ridiculouly well for such cheap pieces, The Marlin 882SQ and the MArlin model 60 semi auto come to mind

I have a winchester 190 its a tube feed I dont like that too much but I love the gun I like semi autosbecause I have a BMF activator from Ruger that basically makes it full auto with a crank on the trigger I can unload 18 bullets in less than 2 seconds. and as far as accuracy goes if you got a .17 take it hunting and the .22 plinking.

I'd vote for the Ruger 10/22 for a semiauto. I have done some over-hauling on my "truck" gun and it puts 10 shots into 1 ragged hole at 50 yards (cheap ammo).