Great little cartridge, I have a Stevens 200 chambered in 6X47 or 6mm-222 Remington Magnum the parent cartridge for the .204 Ruger. I chose the 6X47 just for the little extra case capacity it would give me and the slightly longer neck. Downside for me is limited availability and quality of .222 Rem Mag brass to neck up if you stick with the .223 case you'll never have that problem.
Understand up front the best bullet range for your cartridge is going to be bullets weighing in at 85 grains or less. Yes if you twist the barrel right you could potentially load 100+ grain bullets but if you aren't wanting a single shot rifle, you'll have a tough time trying to get them to fit in a magazine. Go with at least a 1:10 twist, I didn't because I got a deal on a 1:12 barrel but I have a hard time getting bullets over 80 grains to shoot well. HPBT and BT don't stabalize well for when I go over 80 grains.
I chose the Stevens 200 for my action because I decided I was going to put it together myself. I had a pre-fit Savage barrel made by Sin Arms, I rented a set of headspace gages from 4D reamer rentals, and bought a Barrel Nut wrench from Midway. It took me about two hours to put together my Stevens once I had all the parts together, that included installing new recoil lug, head spacing the barrel, replacing the bolt handle, installing a bolt lift kit, and a new trigger.
If I were looking for actions to build, I'd stay with Remington M700 or M7, and Savage M10 actions. You can use other actions and Howa and Weatherby Vanguard come to mind, but they have metric threads and you just have to make sure your smith can thread the barrel. Yes the Mini Mauser action is still being made and imported to the United States as they pop up on gunbroker from time to time, but be careful with them as you will have no real "wiggle" room in the magazine with it or the CZ rifles.