For a good cost effective gun I's start with a Rem 700 Sendero in 338 RUM , have it rechambered to 338 Edge and a Wyatt's box installed as well as a brake then have toe gun bedded , the factory rem trigger can be worked down to crisp clean 2.5lbs pretty easly by a smith. Get a set or rings and a base from Glenn Seekins and the gun will be ready. For the scope Any variable with a top end in the 12-20 power range would work well and remember you get what you pay for , I reciently bought a Nikon Tactical 4-16x50mm adn I coulden't be happier with it super glass for the money as well as the scope by IOR and Nightforce. Expect to pay around $900-$1400 for a good scope with repeatable clicks wheich is what your gonna need for shooting that far.
I would be hard pressed to say that this gun would shoot any more than 1 moa , so goups in the 12-14" range at 1000yds should be do-able.
I'd also plan to get a good range finder and bi-pod.
All of this could probably be had for $2500 or so if you shop around and don't mind buying used things.
But depending on your buget it can go up realy fast from their.
As for the smith , Kirby has a big following here as well as Shawn Carlock , I personaly use Nathan Dagley ,he goes by "308nate" here and his web site is in my signature box.
On a side note , it doesen't take a big ultra mag to kill an elk at 1000yds and unless your shooting a 50 BMG your not gonna knock one down either , a 300 Win mag will kill and Elk at 1000yds with a good bullet. As a matter of fact theirs a great deal on a custom 300 mag in the ads below
Can't blame me for trying can ya