What are important features in a listening chair

whoa, dude......

I had my listening sofa custom designed - deep seat and ottoman for long time comfort,  backrest pillows up up to top of shoulders for good support, but no higher so the sound isn't interfered with around my head.  It worked out great.

Another vote for Eames plus ottoman.

Better pay $5k for a chair than for a cartridge or power cord, I guess.
Not for me, though, I am on the floor too, and anyway, if the music is good it doesn't matter much unless you listen for hours straight which I don't.

Health. Movement. You (not the chair).

Since the focus (so far) has primarily been on comfort and sound quality....

Studies are now showing that standing (at an upright desk) is not much different in impact versus sitting. 

An old school and simple wooden chair that allows for an upright posture. Practice bracing of the abdominals and lower back muscles.