1) Either HD800's or LCD2's (I'm buying both, trying them out, then returning one)
2) I listen to rock for the most part, with both electric and acoustic guitar parts.
3) I've heard that, tonally, tube amps offer a much more musical tone than solid state amps. Additionally, I think a tube amp would help tame the sharp treble of the HD800's
4) I don't care much about connectors. If I can get better sound with a $1000 amp and unbalanced cables, rather than a $800 amp with balanced cables, then that's what I would pick. I suspect the former is the better option.