Personally, just for rabbits and squirrels, I'd be looking at a Marlin 60 or Ruger 10/22. Slap on a Bushnell Banner 3-9x40mm on top of a Marlin 60 and you're only in it for $150-200. The Ruger 10/22 is a detachable mag, but it's super easy to bump your mag release while carrying over your shoulder and lose your mag in the weeds. The Marlin takes longer to reload each time, but it also holds 16.

Pretty much any bulk packed 22 ammo will suit you. I use Remington Gold Bullet ammo, 550rnds for $20. If you're looking for high quality (high priced) ammo, CCI Velocitors, Mini-Mags, or Stingers are great, and offer a LOT of power out of a little 22lr.

My next recommendation would be a Savage 93 .22mag, again with a Bushnell Banner scope. A Nikon Buckmaster would be a step up, or a Bushnell Elite 3200.

I'd also agree that you probably won't be taking a lot of 100yrd shots on squirrels or rabbits, you'll have a lot within 50, and very few at 100.