A .223 is the logical first choice for a .22 centerfire cartridge. There is a wide range of factory ammo and component brass. It is plentiful and can be found on just about any dealer's shelves. There's a lot of reloading data.
As for bolt action rifles, I'd probably pick one with a 1-9" twist. It should handle all but the heaviest bullets well. If I wanted to shoot the heavy match bullets primarily, I'd get the 1-7" twist. There are some 1-12" and a few 1-14" barrels out there. They work well with the shorter, lighter bullets.
Rifles: Savage is a brand some overlook. They shoot and are easy on the budget. I also like the discontinued Remington 788. One can still find them, but the knowing usually hang on to them. I also like the Remington 700VS. I've never tried the CZ 527. They have a good reputation. Some custom makers use the CZ action. I don't like the looks of the detachable magazine protruding from the bottom.
There is the AR-15 platform. I have a Bushmaster lower receiver and a DPMS upper assembly. It has a 16", free-floating, bull barrel. I get sub 1" groups with it.
I had a Ruger No. 1 in .22-250 for a few years. It would reach out and touch them coyotes, crows and pigeons. But around here, the smaller .224s are more practical. A can of powder lasts longer. I'd like to try the .221 Fireball or .222 Remington in the CZ 527.