I'm not sure any headphones can give you a proper 3D sound stage of the sort that you can get with good loudspeakers (especially the LS3/5a). For that, I use recordings of Shostakovitch's string quartets to see how well I can locate (and distinguish between) four instruments.
Although I'm not fond of it as music, Ravel's Bolero is also a good test track for headphones, because of the way the same theme is repeated by many different instruments.
I use Audio-Technica ATH-ANC7b noise-cancelling headphones, but I don't think there's one headset that suits everyone, any more than there's one pair of speakers, or one car....
Any particular recording you would advise? I mean a specific record of known-good quality, preferably on iTunes, Amazon, or similar. I often find myself spending a lot of time listening to different records of the same piece, just to make sure I get a good one.
One strike against this set is that most or possibly all of the CDs have been produced from LPs. Having bought the vinyl versions (twice!) many decades ago, this is good for me but not so good for you.
http://www.amazon.co.uk/Shostakovich-String-Quartets-1-13-D/...
One thing about newer recordings is that they may well be closer-miked and not have such a "natural" sound stage.
The most telling parts are about getting the details from faint instruments, especially at lower volumes. For example the opening part of Beethoven's 9th has very faint sound of violins, and it's often missing on consumer-grade speakers. Ideally I would also compare how wide is the stage and thus how well the instruments are separated, but I don't have the budget for that kind of equipment, if that exists at all.
For my budget, I ended up getting a pair of studio monitors Event 2020bas for speakers, and Etimotic Research as in-ears headphones. YMMV.