If you are looking for a centerfire rifle, any of the 'budget' rifle lines from the major US manufacturers will do well (Ruger American, Savage Axis, Mossberg Patriot).
The design of the Ruger American borrows heavily from the Tikka T3 and has a short 70 degree bolt throw, much like the bolt throw on the old Lee Enfield. It's available in blued or stainless, and with 22" full length and 18" carbine length barrels.
The others are more classic, Mauser based designs. The Savage Axis is a bare bones, budget version of their more expensive model 10 and model 110 rifles. You can build up the rifle as budget allows.
They are all made on CNC machining and are at an accuracy level that 20 or 30 years ago you would have needed to drop a new rifle off at a gunsmith to get close to. They will shoot as good as the shooter can do with the glass they put on it.
As with anything expect to pay as much or more for the glass as you did for the rifle.
Myself, I'm a fan of Savage (model 10 is the short action, model 110 is the long action). Savage, overall, is hard to beat for accuracy in a centerfire bolt action. With a few tools, it's easy for the owner to change barrels and and bolt heads, and hence calibers on one (no gunsmith needed). It's also a simple matter to take the barrel off for threading the muzzle.
For example, on a Savage model 10 short action, to switch from .308 to .22-250 or .260 Remington you simply buy the barrel you want and change the barrel. To go down to .223, you change the barrel, bolt head, and magazine (detachable magazine equipped rifles, which is most of them).
I live in a saltwater environment so my preference is for the stainless, short action, Savage model 16.
Moving up a notch in price from the budget rifles you have the short action Savage model 11 Hog Hunter (.308, .223). The 20" barrel is pre-threaded for a sound suppressor, internal 'blind' magazine, this is one of the few bolt actions made today with iron sights.
A bit higher in price you have the bolt action Mossberg MVP Patrol (.308, .223). It has a handy 16.5" barrel, iron sights, threaded muzzle, the .308 version uses both M-14 and AR-10 mags (off the shelf, unmodified magazines), while the .223 version uses AR-15/M-16 mags.
There is also the bolt action Ruger Gunsite Scout Rifle (.308, .223) available in blued or stainless steel, 16.5" barrel, iron sights, pre-threaded muzzle, and uses AICS single column mags.
NOTE: Why you see a lot of 16.5" barrels on American made rifles is because 16" is legal minimum in the USA for a rifle without special papers and they always cut it a bit over.