I think there is a lot of wisdom in what joe-nwt has said!
I have owned a lot of .22 centrefires rifles, from .22 Hornet to .220 Swift, and including .221 Fireball, .222 Rem, .223 Win, .22-250, .22 Hi-Power, .225 Win, probably others that I am not remembering right now.
In my own experience, the ones that are the most pleasant to reload are the .222 Rem and the .22-250.
I never met a .22-250 that could not shoot anything you fed it, with good accuracy - with the exception of an older lever gun that gave only mediocre accuracy.
I have never seen a shot-out .22 centerfire barrel, although these probably exist since people talk about them all the time. That includes half a dozen rifles in .220 Swift, one of which saw well over a thousand rounds and still the bore, throat, etc were bright and shiny. My opinion is that, for just about any shooter, the likelihood of burning out a barrel is minimal. (Please note I am not talking about bench-rest shooting, where a "shot-out" barrel has groups opening way up to an inch at 200 yards kind of thing......)
I am on the side of the .22-250 for the reasons noted by other posters. It just might be my favourite .22 cf cartridge......
Doug