Originally posted by Masherbrum
1.) 22-250
2.) .243 or .270
All 3 above can also be used for Deer.
Ariansworld
If you are hunting for meat the 22-250 is not a good choice. Neither is the .17, 225 and other "varmint calibers. They tend to do way too much damage. I hunted lots of rabbit as well as varmints with a 22-250. Unless you get a head shot there won't be much "eating" left on the bunny.
They also tend to "blow up" on larger game and cause surface wounds without doing sufficient penetration for a good quick kill. As was already posted a .22, even a center fire may not be legal for larger game.
The .243 and .270 are definitely good choices for deer. Way overkill for rabbits and squirrels though. All 2 are bad choices for any bird hunting.
For what you said in your last post I think what you want is a .22. A nice bolt action would likely have the best accuracy potential but some of the semi's do pretty good. I prefer the Marlin, like I posted earlier, and others have good luck with the Ruger. Try shooting a couple examples and see what feels good to you and what shoots best. Besides what I already said the .22 is cheap to shoot, far more so than any center fire caliber.