Re: my budget .308
If you really want to get better on the cheap. Either buy/rent a 22. Ammo is very inexpensive and it will help you master the fundamentals.
Also recommend shooting in the off hand(standing). This will help you really master trigger control. If you don't allow the trigger to break with that "surprise", it will break exactly out of the black.
First thing they did when I went through school was put us behind the M40X (heavy barreled 22).
It definiteley is a cheap way to get better.