How much $$$$??
Dehan--Long distance shooting + high precision shooting = VERY expensive rifle. Just how much precision are you interested in attaining, and how much $$ are you willing to spend, attaining it? And what is YOUR definition of "deadly accurate"?
I agree with the previous posters, though, that at 800 + yds, shooting skills are paramount. So you will either be very rich, or highly sponsored, or reloading your own ammo, because you will be practicing A LOT.
I also agree with the previous posters that the cartridge involved is not the major issue. Back when surplus .30-'06 ammo was available cheap, that cartridge owned the distance shooting records. Not because it was the best long distance cartridge, but because the distance shooters could afford to practice with surplus ammo. Then .308 Win ammo (or, 7.62x51 if you will) became the cheap surplus ammo, and bingo, the distance shooting records all went to that cartridge. Nowadays there isn't a cheap-surplus-ammo-cartridge suitable for long-range shooting, so the handloads are more important, and the cartridges are more well-suited to the distance shooting.
Military snipers use a lot of .300 Win Mag, .338 Lapua Mag, and .50 BMG, but they don't have to pay for the bbl replacements for their firearms. The 6.5's are MUCH easier on barrels, the ammo is a lot cheaper, even considering reloading, and ballistically the 6.5's have some very nice bullets for long-range shooting. But are you up to spending the $$ to get yourself a Tubb 2000 rifle? And practicing enough to make the investment worth while?