I don't have a rack for my headphones per se.
Although I do have a rack for my system. Everything shares the one rack. I have a specially manufactured wall rack for my Rega turntable.
My headphones are usually stored, hanging from one of the supports on the rack and Itake them off there when I need to use them. I don't get too anal on the storage of my 'phones.
I do recommend that to get the most from your system, a decent rack is a must.
Personally I use a double-width three-shelf stand with quarter inch plate glass with a tubular steel frontage that has been chrome finished. The stand was manufactured by Ash Designs here in the UK. I got mine half price as it was an ex-demo unit from a local dealer. The difference in the sound when I got it was very clearly audible - to say I was shocked was an understatement.
The system has changed since this photo but it give an idea of the rack. Sort of?
Sound As Ever
Listening to OH SUSANNA - I've Got Dreams To Remember
via Krell MD10/Studio DAC thru Stax Lambda Nova 'Phones