I'm very late in the game and suppose the OP has purchased his setup by now. But anyway, I own some of the components he's talking about so here's my 2 cents:
Firstly, I think you need to make a decision about how you like your sound signature and what the quality of the music you typically listen to is. In function of that I'd draw up a shortlist of headphones and audition them; once you decide on the headphones, find a DAC/AMP combo that handles them well. The above assumes that you won't turn into an addict like most of us here who have various sets of headphones/amps and dacs sitting around.
I own -see signature- the HD-800 and the V800/V200 combo. The HD-800 are truly great headphones and offer unparalleled soundstage and imaging, BUT:
- Ruthlessly accurate, to the point of distraction if you listen to less than pristine recordings. I don't know about your genres but I listen mainly to classical and can testify to the fact that absolute precision in reproducing everything that can be heard is sometimes less than desirable, especially when listening to old recordings.
- Very analytical, I'd say they're almost more for detailed study of music than for relaxed enjoyment
- Picky as for the amp that drives them, some combo's work great, others are really unenjoyable. That being said, the V800/V200 combo pairs VERY nicely with them -I don't think many will dissent about this- and although they don't really colour the sound they do add a touch of warmth to the HD-800, not a bad thing imho. I auditioned them with the conductor and found this emphasised their analytical nature (it's a very 'fast' combo) and made the sound quite cold with the HD-800. The conductor's a good amp imho but it accentuates some already extreme properties of the HD-800 and takes things too far.
- There's the Sennheiser tax to contend with
My favourite cans are the HiFiMan HE-500, they pair well with the Violectric combo, are not monsters to drive such as the HE-6 and great with vocals. Downside of all the HifiMan cans are weight and comfort but as far as bang/buck goes you'll be hard pressed to find better value than the HE-500 imho.
FWIW: I've never auditioned the LCD's but people whom I trust tell me that they pair nicely with the Violectric combo.
But above all: if at all possible, decide for yourself and audition the cans. Only you can decide, this site can give an indication and be very helpful in making a shortlist but beware of anyone who comes to you bearing 'the' end-all solution. There's no such thing as a headphone that's best in everything, it's always a compromise. Even within classical music I often find myself switching between the HE-500 (smaller ensembles, vocals) and the HD-800 for large concertos.