I have never even attempted a shot at 800 yards, but I understand that my Nightforce NXS (I think 5.5x-22x-56mm which back then cost me noticeably over $1,000) is one of the best scopes for such long range shooting, especially when used on extremely high power cartridges like the 50 BMG.
Nonetheless, I understand that keeping costs down is important, but don't go to cheap. I own a Bushnell Elite 4200 in 4x-16x-50mm and it's one of my favorite scopes. This scope has been very accurate, and very reliable for me. The Nikon Monarch in a fairly similar power range is also a great choice. These scopes are what I call "Upper Middle Class" scopes. They aren't Swavorski or Zeiss, but at less than half the price, they are truly an excellent value and their optics are fairly close. Put in other words, I personally do not believe that by paying double the money for a Swavorski or Zeiss, that you are truly getting twice better optics, quality, and performance.
Also in my opinion, you can go a LITTLE cheaper, like the Bushnell Elite 3200 series (which I call the "Middle Class" of scopes), but I would not recommend that you go cheaper than this class of scopes....especially if you are considering shooting at such long distances.
Of course, Bushnell now has the 6500 series which I understand is an improved version of the 4200 series.