budget sniper rifle
With a sniper rifle, the sky is the limit, money-wise. My son has a Model 700 heavy barrel, with a generation (3 or 4) scope, brand unknown, attached, that is controlled by an electronic "dope box". Shoots 1000 yard matches with it. Son has, in the neighborhood of $4500 in the rifle, and I am sure he is not through tricking it out!
Having said all that, go military surplus. There are a multitude of rifles available out there that will put you on target at 500+ yards, dressed with a good scope. Everyone will throw out a favorite brand, that they have been successful with and are satisfied with the performance.
The U S Marine Corps, refused to release the 1903-A3 from service use until 1974. Why, because they relied on it as a solid base for a sniper rifle. Even in the Twenty-First Century, the Marines are going back into the warehouses and using M-14's for sniper service, in Afghanistan..I think the M-14 was replaced by the AR15/M16 in the early 1960's. Tried and true Performance, in the worlds harshest environs..