In order to play music from your phone to the headset, it will need to use 3.5mm connectors like headphones do. This means that they won't have any controls with the exception of volume control and muting in some cases. This will limit your options.
I always recommend a Sennheiser headset before anything if they can afford it. Since you haven't mentioned you price range, I'm just going to throw it out there. A mobile can power the PC360's (G4ME ONE) well enough, but it won't be able to power the PC350's (G4ME ZERO). I haven't looked too much into their lower end headsets, but I'm pretty sure that they have an impedence of 32ohms, so your phone would be able to power them just fine.
The Logitech G430's have 3.5mm connectors and comes with a USB sound card that you plug into the computer. A friend of mine got his about a month ago and he is happy with them. He listens to music on his phone occasionally with them, but primarily plays PC games and Skypes with them.
If memory serves me well, I believe Corsair makes both a USB and 3.5mm version of the Vengeance 1500's. I haven't personally used these, but have heard pretty good things about them.
Keep in mind, these are the headsets and brands that I am most familiar with, so I'm sure there are better options out there. None of these have removable microphones or retractable microphones.
The only thing that I want to say regarding other brands is stay away from Razer. Some people will swear by them, but every Razer headset I have used (luckily none of them were mine) either sounded terrible, felt extremely cheap, didn't work, or barely worked.