With that kind of budget,you likely need to look at a savage or marlin bolt action (in .223,.22-250,.243,or 25-06) and use the rest on a good scope. I'm pretty sure the marlin don't come in smaller calibers however but just got 1 in shop and am impressed with it for the price. The cheapest "varmit" scope I've had good success with is the weaver V16. It's a 4x-16x-42mm scope with tall turrets,very good optics and tracking(adjustment reliability) for the price. They run289$ at
www.swfa.com. Now,with about 400$ or less in rifle,and a lil less than 300$ in scope,you'll have enough left over for mounts/rings and some ammo.