recoil
Another vote for a modest caliber and be wary of the '06, especially in a carbine like the light, short CZ550 Bavarian. Certainly a quality item, to last your lifetime, your kids and grandkids too. But blast, flash and recoil, real or perceived, is pretty high in a short light '06. I've got a similar rifle in '06, and do not run it full power, it's just too darn obnoxious. And I've learned I don't really have to, as it kills just fine running about .300 Savage levels. As noted by others, the jump from a .22 to '06 is pretty dramatic, and in the carbine, even more so. I don't see '06 as a training or paper punching round for the most part either , high power match shooting excluded.
For punching paper now, and maybe deer in the future, and you are truly limited to one centerfire rifle, I would agree with the other recommendations of .243.
However, let me add that a bolt .223 is a great step up from .22 lr as a trainer, and ammo is plentiful and comparitivly affordable. There are a lot of price point .223 bolt rifles on the market these days that can give you centerfire practice and ballistics, without high cost, recoil and blast. You will be able to shoot a bunch of .223 for the cost of a good deal less amount of '06 ......or........ .243 for that matter. But I do not see the .223 as an ideal deer round.......which means you would need a heavier game rifle if the opportunity develops for you to hunt.