The "budget rifle" question comes up over and over again ... I thought I'd share what I have done.
This is a savage hawg hunter in .223. Rifle was right around $400. chunked the iron sights, adjusted the trigger down to 2.25 lbs, placed it in a B&C stock (drop-in fit). Total cost about $660? Mine's a .223 but you could do the same thing in .308:
It is shooting consistent 3/4" 5-shot groups @ 100 with no load development, sometimes a little better:
only downside is that the savage blind magazine sux. It's a bear to get it out of the original stock, transfer it over to the B&C, and have everything work correctly (at least in my example). and if you want detachable magazines, there's more work to be done.
Another option is a bone stock Remington 700P in .308 for $900ish:
3 shots at 100:
10 shots at 100:
Both of these need better optics than what I have on them, but that's a subject for a different thread ...
This is a savage hawg hunter in .223. Rifle was right around $400. chunked the iron sights, adjusted the trigger down to 2.25 lbs, placed it in a B&C stock (drop-in fit). Total cost about $660? Mine's a .223 but you could do the same thing in .308:

It is shooting consistent 3/4" 5-shot groups @ 100 with no load development, sometimes a little better:

only downside is that the savage blind magazine sux. It's a bear to get it out of the original stock, transfer it over to the B&C, and have everything work correctly (at least in my example). and if you want detachable magazines, there's more work to be done.
Another option is a bone stock Remington 700P in .308 for $900ish:

3 shots at 100:

10 shots at 100:

Both of these need better optics than what I have on them, but that's a subject for a different thread ...