If you want a little lighter package to tote all day, the 20 works fine too. For either gauge I like 7 1/2 or 8 for squirrels and 7 1/2 if rabbits are close 6 if they tend to be a little farther out in that area. If you don't mind recoil, or willing to put a nice pad on, and can get good enough at the shooting, A single shot 20 or 12 really is a sweet gun. I hunted for the first 8 years of my life with only a bolt action .410 and the line... "Beware of a guy with only one gun" rung true for me. Squirrel hunting was fun for spotting the buggers but my buddies bragged up my shooting by truly stating "Brent is the only kid we ever seen that could shoot 28 squirrels with 25 shots."
A .22 is fine for a challenge... I prefer the bolt action for the "Big Boy" rifle feel but love a marlin 60 when feeling lazy. For pistols, I know several guys who love their Ruger MK series with scope or "halo" optics for rabbit. Head shots are a must if for the pot. The additional challenge to plan your shot for back stop is fun. For tree rats you have to set up so the bullet enters tree trunk or thick limb every time to feel comfortable about errant projectiles.