Pretty much, the only thing that will make it cross compatible is either outright getting Xbox branded set (I wouldnt do this), or getting yourself a pair with low impedance, connects via 3.5mm jack with an adapter of some kind.
Impedance is just a measure of electrical resistance, the lower the impedance the less electrical energy you need to achieve a certain volume. High impedance headphones could cause problems as an Xbox unlike with a PC you cant throw an amp at it if its too weak. Most headphones will be fine though, if impedance is high the product specs should let you know (above 64ohms is considered high).
You want a 3.5mm jack because getting a USB one introduces software and drivers, each of which just makes it annoying to move between devices and limits compatibility.
Adapter is the difficult bit. 3.5mm should plug into whatever PC you can find, the consoles not so much. You either need a USB to 3.5mm adapter and one that is certified to work on Xbox's, or your display needs to offer a 3.5mm jack to play the audio it receives through the HDMI cable.
"Surround Sound" headphones are pointless. You can cram in 7 speakers into a pair of headphones, doesnt change that they are all literally next to each other.