RE: .22 for coon and rabbits
Rifle: Ruger 77/22 bolt action or model 96 if you want a lever.
Handgun: Ruger Single-Six (available in various barrel lengths, blued or stainless)
Recommend stainless with 5-1/2" barrel.
Other possibilities for a rifle would be Remington 572 pump action, or Marlin 39A lever (or a 39M if you can find one without having to pay too much for it).