Honestly with a sub $1000 budget, not sure you can really go wrong. The market has a lot of sub moa guns in that price range. Features, weight, etc. will probably be your deciding factor.m
Sub $1000 for the base gun and 10 pounds or less
Im looking at these
And also the ruger American predator
I would look towards Howa/Weatherby Vanguard, Bergara and Tikka but the Savage is a fine rifle.
Heck, I won a 30-06 Savage Axis in a raffle ($400? gun) and the first three rounds out of the gun were at one moa shooting off a wooden block with Remington Core-lokt ammo. So were the last three rounds - 'cause that's all I shoot it....
As to caliber, anything 6mm/243 on up. I prefer the intermediates - 6.5 creedmoor, .270, 7mm but my youngest son has gravitated to 30-06. As a matter of fact, he has hunted with an old Remington 742 in the 30-06 that last few years. Even that old gun will hold about 1.5 moa until the barrel gets some heat in it. 30-06 hits hard....