223 Rem is one of the shooting industries most versatile chambering.... I loved my 222's of which I had a few but the 223 will do everything the 222 will do and then some.
Now if you really want a 222, prefit match barrels are possible so it is an easy thing to create but you aren't likely to find any factory rifles currently produced in this chambering.
One of the nicest rifles I have owned was a Rem 700 classic in a 222Rem... if you can find one in good/like new condition, they can be a fantastic rifle. Same goes for the Brno Fox.. mine had a double set trigger too. A couple of golden oldies. The Savage 340 is a clunky beast but the few I had actually shot much better then I would have expected from such a humble rifle.
Today, I am only into the 223 Rem.. it is just so much easier and I do enjoy shooting LR with it.
Just remember that you can make 222 Rem brass from 223 Rem brass so brass supply can be plentiful and cheap if you decide you want to wildcat yourself some brass.
As was mentioned, you can easily download a 223 Rem to match a 222 Rem or anything smaller... brass then lasts as long as you are willing to anneal.
Enjoy either choice.
Jerry