[Aleksi]

Although the Axe-Fx doesn't have a headphone out, the line outs are plenty strong to drive pretty much any headphones (I believe Cliff Chase, the creator of the Axe-Fx, said so on the official forum). You will need an adapter with two mono plugs on one end and whatever is appropriate for your headphones on the other. As for the sound through headphones, for my taste headphones always sound too direct and in your face compared to speakers. Of course you can use the fantastic reverb in the Axe to rectify this. I assume you have a set of speakers at your apartment? You could try it through those as well. The Axe sounds great through good speakers, even at low volumes.

When recording direct you should monitor through your sound card, since you'll only hear the Axe if you plug your headphones into it.

 

[Aleksi]

The Axe-Fx isn't an audio interface, so you'll need a separate one.

 

[Aleksi]

I'd go with an external interface for the convenience. Also, they won't pick up noise from inside your PC. The Fast Track Pro is probably enough for you. I assume you'll only record vocals and guitars, neither of which needs more than two inputs, and The Fast Track Ultra probably has the same basic components as the Pro, so there won't be a difference in sound quality. The Pro also has MIDI I/O which you can use to update the firmware on your Axe-Fx, edit patches on your PC and back up presets.