Definitely spend some time over at head-fi.org.
My answer is: It depends. I have different headphones for home use vs. traveling.
At home, I have an older pair of Sennheiser HD 650 cans connected to a Crown D-45A amplifier connected to a DAC. Yep, 25 watts per ear. Very airy/open sounding. They're also open-back, so absolutely rubbish for travel, as all of the outside noise will be coming in, and my seatmates will be hearing everything I'm hearing in high-fidelity.
For travel, Bose QC25s. Compared to the HD650s, the Bose definitely don't sound good, but the noise cancelling is very good, and when traveling that's what matters most. I got them on sale for $125, which was well worth it.
If you're focused on sound quality, sadly, hardwired is the only way to go. Bluetooth compression does a number on the audio.