I would get a .22 or a .223 for what you are talking about. .22 is so much less money, even buying bricks of $80 standard velocity match ammo, and you learn a ton about doping wind with it, even just pushing it to 100 yards. .223 is less than any other centerfire to shoot, and you can reach out to 1000 yards with the right rig and ammo. Plus it gives you a coyote killing rifle with next to no recoil that just about anybody can shoot and feel accomplished with in a short period of time.
I don't have a lot of money in my current bolt rifles: a Savage MKII heavy target barrel .22 and a Savage 11 .243. Both need better stocks. I'm auditioning a new scope on the .243 right now to play longer range and coyote hunting with, but I bet I'm back to my lighter, more compact Burris 3-9 by the time deer season comes back around. I'll either keep the PA 4-14 FFP mil dot as a second scope for swapping over when I want to do those things, put it on a new dedicated long range rig, or pop it on the .22 and get something higher end later.
I like Savage, but if I were doing this again, or getting the .270 or 6.5CM I'm thinking about, I'd be leaning toward a Weatherby Vanguard or Howa 1500. Don't need a new trigger, can live with the stock (especially on the Weatherby).