after reading some more, thought I'd add some more to this thread.
No matter what optics you choose, you need to mount them correctly.. Rings are never ever really true and they will affect scopes (accuracy) negatively.. They need to be lapped Buy a Sinclair kit, and buy horizontal cut rings and be done...
As much as many will disagree with me,if your wanting a 1000 yard gun the MAGNUM must be attached! With 338 being the king. 300 next 7 is marginal but is a performer at greater distance.
proper bullet weight ,powder and charge with proper primer and case must also be perfectly matched to the rifle.
To keep things under a grand,you have to find a good used rifle deal you can work with preferably one with 26' a heavy barrel.
Find a Choate varmint or tactical stock
I also use a Trigger shoe (I'm old school in many ways) Paint ballers are a good source to find aluminum shoes on the cheap, some jewler's file work is needed for fit up.
Barrel wise if its "shot out" look into cutting off two inches off of chamber side and have it re-reamed MANY times this will allow another truck load of bullets to be shot through it accurately it's a real money saver. Until you're ready to install a KRIEGER BARREL. (I'm a fan boi
Did I mention the importance of lapping scope rings?