Videos will be the main data usage along with downloading large files or lots of music, most other things should be OK. Check what kind of data cap it is, some networks let you go over but throttle your connection. If it’s the sort of cap where they cut you off or charge you they should have a webpage where you can check how much you’ve used.
If you’ve got wifi at home/work enable it on your phone, that’ll cut down on your limited data usage.
Headphones: whatever you’d use with any other music player, there’s probably loads of recommendations on this forum depending on what kind you want (e.g. discrete in-ear, or massive over-ear ones).