At home, I tend to listen to music loudly and freely throughout the house. Easy to do when you don't have a partner or housemates to think about. I actually have several headphones - some older Sony cans that are comfy as hell, a pair of those shiny red Sony over-ear cans, and a pair of overear ones that are similar, but really fucking uncomfortable.
I don't actually like cans for convenience or comfort, because when you need to take them off, you either have cans wedged under your chin, or have to take them off and deal with the cabling. Storing them away is a pain in the arse as well. So I prefer my old Sennheiser earbuds, since they're convenient, sound decent, and can be shoved in your pocket.
As for genres, my #musicmonday posts should be giving you an idea of my favourites, though I love good music, not particular genres. I could be listening to rockabilly one day, hip hop the next, and dark country the day after - whatever my mood strikes.