Well, basically you'll want a soundcard that's as powerful (or hopefully more so) than the GNX, since it's going to be used by your DAW to route all the plug-ins and audio in and out of it at low latency.
The Axe-FX would be going into and coming out of it, and any audio or VSTis in your DAW would be coming out of it. So you'd want the headphones plugged into its output to hear everything. If you plugged into the Axe-FX's output, you wouldn't hear the other stuff.
Something simple like the Audiophile series will do the job. I use an M-Audio Delta 44. It has four inputs (more than I need, since I never record live drums) and four outputs. You could easily get something for $60 or less.
It is worth mentioning that if you don't buy one with a specific headphone out (the Delta 44, for example, doesn't have a headphone out), you'll need something to boost the signal before the headphones. You could plug the output of the soundcard into your home stereo amplifier and then headphones into that.
Also, it might be possible to use the Axe-FX as your soundcard in the same way you can with your GNX or with a Pod. But not owning one and never having even seen one, I wouldn't know. If you can, then you won't need a soundcard. The Axe could do it all.
Thanks for all the info and advice. Very useful stuff. :yesway:
The GNX3000 can record guitars, bass, vocals, keyboards, and I've been using it as an audio interface for recording, but I think it might be overkill to try recording the Axe-FX through it.
I checked out M-Audio and it seemed that the options were: USB-based audio interfaces (such as the Fast Track and the MobilePre USB), PCI Audio interfaces (such as the Audiophile 192 and the Delta series stuff), and there were the MIDI interfaces.
Which of those would you guys recommend? USB-based or PCI Audio? (My PC doesn't have Firewire and I doubt I could use the MIDI interfaces for everything).
I already reserved an Axe-FX Ultra at a store near where I work.
And I think I'll be using some Bose speakers that don't color the sound with unwanted EQ. :yesway:
Thanks for all the advice, guys. (I tried to rep you, Cassidy, but it seems I need to keep spreading the rep around before I can rep you again).