Marlin 795 can compete with the CZ bolt
At the budget you mentioned, I think a Marlin 795 is the way to go. I have both that and a CZ 455 American. I qualified with them both at Appleseed. I haven't done a detailed accuracy comparison with best ammo for each, but they are in the neighborhood. I think I can get a dime sized 5-shot group at 50 yards with either from prone if they are getting the right ammo. Should get you going until you scrounge up $2k for an Anschutz or something.
I think you could get a 795 with scope, base and rings for what you were budgeted, but the glass would be nothing special. 4x magnification is all you need (probably) out to 50, maybe 100.
"Jeez, man, what's another word for 'stupid?'"
"Tactical." -Tom Servo
Marlin 795, 795ss, 39A Mountie, CZ-455 American, CZ-452 Scout, CZ-75 Kadet, AOM160 M1 Carbine, USGI M1 Carbine, M1 Garand, Dan Wesson PM7 1911