I really like the .222 out of the rounds you've listed, and the .223 is nice too. Whether any of them are too much for rabbits depends on whether you want to eat the rabbit or not. If you don't shoot a rabbit in the head, anything much bigger than the .22 hornet isn't going to leave much rabbit behind. You might also want to consider the .221 fireball, which is being offered by Remington and CZ in new rifles. I'm not very familiar with the .22 PPC, but I don't think there's much factory ammo available for it.

I would consider a .223. Cheap to load or buy. If you are going to shoot at plus a hundred yards be sure to get a good scope. Infact you probally will spend more on a good scope than a rifle.

I have found when shooting at rabbits, foxes and birds that I would like a little more range than the 22 rim fire has to offer. I guess I'd like to get them at 100m-150m+ instead of 40m-50m. The next size up that I have is a 243 which is far too much cartridge.

Cartridges I am considering include 22 hornet, 218 bee, 222, 223 and 22ppc. Head shots are a definite advantage so I have been leaning toward the accuracy of the 222 or 22ppc. What rifles has the ppc been available in? Is there much factory ammo available? If need be I can load for it but more than likely I won't have the time. Is it too much for rabbit shooting?

Any other suggestions?

nobody can live without a .223, or a .308