My advise to you is to spend some time reading and investigating here on the GTA before you commit to any one gun. Your mind might change 50 times once you see what all is out there. But, worry not, This is just the beginning. You'll be a multiple gun owner soon enough.Richard
You may also wish to look at the MSP's. The older Benjiman 392's are good. The Daisy 22SG/22X would more than do what you need (My main hunting rifle now). Or if you are dead set on something new there is the Crosman 2289g with a few power mods a longer barrel and a steel breach the 2289g is still under $100 total.
just over your price, XS28 , makes darn near 28fpe and will protect chickens et al. .John