For mixing/mastering primarily via headphones you should try to audition a couple of the external sound interfaces, bring your 6XX with you and ask if you can plug them in at the store. Preferrably bring some of your music as well. You want to make sure the headphone amp in the interface is up to the task. 6XX are 300 ohms Z if im not mistaken, so make sure you're listening at a comfortable level and have headroom left to spare.
I bought a E-MU Tracker Pre used very cheaply and was positively surprised at both the SQ and drive of the built-in amp., driving my 58X. Software drivers are always tricky for old hardware, and you do not state if you're on macOS or Windoze, fortunately for me, there is a community driver for the E-MU for Mac.
You could check out Avid Mbox Pro 3, should be around 100euro/dollars/pound used, and seems to come highly recommended, i used a Digidesign Digi001 way back and it was a solid performer.
Gpod Luck and let us know how it goes!