RE: What kind of 30-06 is best for my budget?
I once had a BAR, in .308 Win. It would place the first two rounds close together, and the third & subsequent shots would walk away. However, I have heard that the BAR's are accurate, good rifles. Maybe your problem could be cured by finding the right ammo?
Anyway, if you want to replace it with a rifle having more potential to be accurate, I suggest a good bolt action.
Savages have a good rep. for accuracy, as have the Weatherby Vanguards-the latter carry an accuracy guarantee.....