The HD800 is a terrific headphone - I spent quite a while agonizing over whether I should go with an Audeze offering or the HD800. In the end, I wound up with the LCD-X - there's something about the effortless way the LCD-X renders vocals which won me over - though if I could afford both, I'd have gotten a HD800 as well in a heartbeat; the soundstage offered by the HD800 is the largest and most wonderful I've ever heard, and it does just about everything right.
That being said - even a new pair of HD800s will leave you a grand for a DAC/amp. I owned a Benchmark DAC1 for a decade or so - it retails at $995, leaving you with $5 left over for an album. The Benchmark is about as neutral as they come, and the integrated headphone amp is excellent - they should serve you well for years.
Some claim that a very neutral headphone+very neutral dac/amp sounds too bright - well, you may also find it to be so, but if you are not opposed to EQ on principle, it seems like a good idea to ensure your starting point is as close to being 'right' (As in, sonically - not necessarily according to your taste) as you possibly can get it, then EQ from there - at least to me. :)