For a bolt action, you can get a new Remington or Savage rifle that is pretty darn accurate straight out to the box. I don't own a Savage but they have a reputation of being the best bang/$$$ in terms of accuracy.
x2
My Remington 700 had pretty good grouping at 100 yards right out of the box. I paid just over $300 for it after tax. If you really want to add stuff, you have another $700 for a bipod and a new optic (gun already comes with one, but it is not the best)