I am interested in over the ear, either closed back or open but I think I would prefer open due to already owning closed back headphones (below). They must be either wireless or have a removable 3.5mm cable/female 3.5mm socket on the headphones so I can make them wireless. I would ultimately like wireless and an upgrade in sound from my current headphones.
I already own a Hyper x cloud 2 headset which has good sound for gaming but I would like something a bit better for music.
Additionally, if there are headphones that are much better but are more expensive than the above budget, I could be convinced to spend more so please mention them. I think my limit would have to be around $250 though as it's not something I need, just want :)