No need to go big caliber for those ranges. In fact it might be overkill to go too big to shoot 1k with a big bore as the ammo cost will suck your wallet dry.

Big question, do you reload and do you have a solid background in reloading? If not, stay with the calibers that are offering high quality factory ammo for long distance shooting, primarily .308 Win. If you have reloading mo-jo and the equipment, .260 Rem. If you are going to get really fancy, 6.5-248.

There are plenty of reputable custom rifle makers out there in the 3 to 4k amount; check out sniper's hide a bit and you will find info on them all. savage and Rem are the two factory rifles that seem to work pretty damn well for a cheaper avenue. There are a few local guys building some nice rifles too.

Don't skimp on optics. Anything less than $800 is not going to be a fun time at 800 yds. Cry once and be happy. Get a good scope from the higher end manufacturer with a distance ranging reticle, adjustable knobs, solidly built and repeatable and above all excellent glass and be happy (ya, I know it's a run-on, and I'm not changing it...). Nightforce is a damn good scope for the middle of the ground price. There are a few others that do well too, once again Snipers hide has this area all but covered too.

stepping off into long distance rifle shooting looks like a basic step, but it can be expensive to do right. It takes an ass load of ammo and practice to get it right too. Just learning how to dope the wind is enough to make you crawl up into the fetal position and cry at times.

Highly precise long distance shooting is one of those things where the equipment is just as important as the shooting skill IMO. Then add to it, the reloading skill. You really have to reload for it with the mind set of absolute anal retentiveness to get the ammo consistent.