I won't get into the suitability of using a .22 centerfire for deer hunting. I freely admit to a bit of a negative attittude about that, if other choices are available.
That said, I doubt that the 55-grain bullet is really a good idea. SFAIK, any bullets below 60 or so grains are designed as varmint bullets; they're designed to "blow up" readily on small critters such as prairie dogs and woodchucks. They'll work on coyotes, of course.
Modern days' R&D and bullet technology is such that bullets of around 65 and 70 grains will work on larger animals such as deer. Thicker jackets, better penetration.
Range limits? Personally, with a relatively marginal bullet, I'd say the limit should be that at which you begin to lose the ability to make that perfect or near-perfect shot. For me, with a .243, my self-imposed limit is roughly 200 yards. That's about the limit for a neck shot from a hasty rest in the field, or a specific heart shot on a cross-body view. I won't take an angling shot with the .243 like I would with my '06.
FWIW, Art