Pretty much any gun.
I've put together several bolt guns, all my target bolt guns.
Buy the action. Find a stock and inlet it. Find a barrel, chamber, thread and crown it.
I have a lathe and milling machine but you don't really need them. Several companies (brownells, midway, etc.) sell threaded barrels for Mausers, Remington, and other actions. They are mostly chambered, you just have to get a chamber reamer, and head space gages (these can be rented) and finish chambering them.
The quality depends on you, how much time and care you put into the project.
I prefer wood stocks but they take a bit more work. There are tons of composit stocks out there just about for any guy you choose and any price range.
You want a cheap, but quality build, start with a mauser action. They can be had fairly reasonable from SARCO or other on line outfits, Less then 100 bucks. You can get a composit stock for less then $100 also. Midway has tons of pre chambered Shilan Match barrels, in just about any caliber you can think of for $240.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071