Amongst non-expensive firearms and ammo there is one very good choice for long range shooting, which would be the 270 WSM and that Barnes all-copper 140 gr bullet. No muzzle brakes needed, recoil is about like a light 308 bolt action, and the less dense copper bullet has a huge ballistic coeffient. Load to about 3300 - 3400 fps. Obvious choice for a rifle would be that heavy barreled Savage which can be bought for around 600 on Gunbroker.
Guys used to spe3nd more on scopes than on rifles and that's no longer necessary, the latest generation of Chinese tactical scopes is more than adequate for something like that. The idea would be to get on either gunbroker or ebay and buy the best Chinese tactical scope you can find, two or three hundred dollars or thereabouts.
Guys used to spe3nd more on scopes than on rifles and that's no longer necessary You're not actually trying to hit a man-sized target lurking behind trees 1000m away are you?
BTW: the upper photo was from ~1000m (to target at top arrow), bottom from ~600m (same target, so imagine the target appearing about 1/2 the size).