Ok, you first question was what gun to get. I am assuming this will be your first gun, am I right? If so, a bolt action or single shot would be the best to get. I would reccomend getting a Marlin or Savage bolt action. Another that comes to mind would be an H&R Single shot which allows you to switch barrels from .22 lr, to 22 mag, to the new 17 HMR later. I believe you can also shoot the cb shorts in the single shots, however, make sure if you do, that you clean the chamber before going back to longer shells, or the long shells will get stuck in the chamber because of powder residue buildup. Your best bet to avoid this would be to stick with regular .22 lr shells. The CCI mini mag hollow points should work for everything you mentioned. And don't think that any bullet will not go through even the biggest rabbit you will come across. Make sure it is legal to shoot where you live and that you have a safe area to shoot because bullets will go through everything you mentioned and still have enough velocity and energy to ricochet and cause damage elsewhere.

Here is a pic of my H&R .223 that I shoot at jack rabbits. A LOT more powerful than the .22, but the gun is the same as I mentioned earlier.



And a pic of three jack rabbits I got this weekend, ranges were 50-100 yds or so.