I build DG rifles on 3 actions, Mauser 98's, Win Model 70's (new or Pre '64) and CZ 550 Safari Magnums. The CZ has been discontinued, I buy up whatever I can find.
As to left hand, the Win and CZ both come in LH, albeit in less calibre numbers.
I have bought and built Rem 700 DG cartridge guns, my last was a AWR I used as a donor, was chambered in 416RM and booted a lot, the customer wasn't impressed with it and neither was I. Just couldn't build it heavy enough. If it had a Sendero contour it may have had enough heft, but it wore a #3 contour.
I really like Ruger No. 1's for DG, but many folks don't like them.
I have 2 myself, one in 404 Jeffrey and another in 470NE. I have other barrels in 500NE and 577NE.
I guess it depends on what you want to do with the rifle.
Cheers.