I've used headphones with the built-in headphone amps in the OmegaStar and Insight preamps. I have also used a box I made up years ago to allow headphones to be driven by a power amp. (I based it on plans in Audio Basics.)
I've used the Grado SR-80, Sony MDR-EX71SL (recommended by Linkwitz), Yamaha HP-1, and also the AKG K240.
The built-in headphone circuits sound at least as good as using the power amp, and are less noisy too.
I think I would also say that built-in headphone amps sound better than a number of other dedicated headphone amps I've listened to.
If I were living in a small apartment, I think I could be quite happy with an AVA DAC, preamp, and a good set of headphones.