I have a Savage 110 in .30-06 while each of my sons have Savage 111’s in 7mm-08. All with AccuTriggers. Accuracy is phenomenal. I can’t tell you how much I like that 7mm-08 round. My Dad has hunted with that round in a Browning BLR for years and it is simply a game getter. It just seems the critters are “dead before they hit the ground” with that round more than any other in my experience. Probably too light for elk, tho and unless you load your own, costlier than the .308.
Anyway, I picked up a never fired Ruger M77 in .25-06 last year at auction. I am very impressed with its action. Very robust and clean. You can still get great deals in the used and auction markets if you are patient. Well within your price point.
Don’t Forget...!.. If you consider Savage... gotta get the AccuTrigger!
Good Luck!