A Tikka T3x in 6.5C will have much less recoil than your old .30-06 did. I bought a T3X in 6.5C after a serious shoulder injury and reconstructive surgery made it too painful to shoot my .300WM. I can shoot 4 boxes of ammo at the range with no soreness. My flinch is gone and I can spot my own shots. I have now killed 2 elk and 3 mule deer with it out to 400 yards. I just had it cut down to 18" and threaded for a suppressor. and I'm still under your budget.I actually had the 30-06 threaded which did help with the recoil. The magazine issue ultimately made me get rid of the rifle. I would prefer to not need the MB though. As much as I know I need to put in ear pro every time, I have often found myself leaving them out when something walks out in front of me.