You can get Ruger American and optics for under $500. They're supposed to be very accurate out of the box. I've heard people claiming .75-1.5MOA with factory loads.
I spent $650 on my first rifle last year. Got a Ruger M77, optics, ammo, cleaning kit, and a sling. I hear many claims that "Rugers are not accurate" mine shot under 1MOA with factory ammo. Out of the box, stock. With a run of the mill 3x-9x-40mm