Have a Leopold mark 4 4.5-14x50
Should be OK for starters. See how it does on a "tall target test" that will confirm that it was installed level and tracks properly, giving you the intended number of MOA of turret tracking (not always the case)! You also may want to add a scope level - inexpensive "insurance" against cant errors that result in horizontal dispersion at moderate to longer ranges. I like the US Optics rail-mounted bubble level and the Vortex level.
Don't skip the tall target test - it's quick, cheap, and tells you a lot. You need this info plus a reliable 100 yard zero to eliminate some of the basic variables to be able to generate consistent hits at longer ranges, no matter what rifle / scope combination you choose.
Also, your original post didn't mention if you handload or not. If no, reserve some budget for match-grade ammo and save the brass for future reloading. If yes, then plan to purchase any missing equipment (neck-sizing or collet dies if you're reloading for the same bolt action rifle), projectiles, powder, primers, and overall length gauge plus brass and bullet comparators. These bits are not overly pricey and make big differences.
If handloading, access to a chronograph is critical.
The entire "shooting system" is only as good as the weakest variable between shooter/technique, rifle/optics, and ammunition (velocity and standard deviation as an indicator of consistency).