Personally for a adding a budget level bolt rifle is the Ruger American Standard in 30-06. Can be purchased at great deals, I bought mine on sale at Walmart for $199.00
For ammo is Hornady American Whitetail 30-06 150 gr Interlock #8108 muzzle fps is 2910 with 400 yds -23.5 below line of sight.
Mine shoots under well under 2 inch groups at 200 yds. At 71 my eye sight fails due to cataract surgery.
With a zero at 250 you'll be 42 inches low at 500.
