I don't do voice (song) recording but I do work online and need an appropriate headset. I'm not sure if it would be different for singing, but for what you said you need it for I don't think so. I'm not sure but you might actually want a headset so that you can listen to the music and not have it picked up in your mic.
I use this
Normally you are going to find that most logitech over $50 are going to be good.
I prefer the audio plugs but some people use usb. Usually if your USB isn't plugged in and you start an application you will need to plug your mic in and restart the application to get your mic working. I had to do that one too many times and switched to just using the audio plugs. I did find that with usb you can use both your speakers (for music) and your USB (for talking) instead of both over usb. (which probably wouldn't be good for recording anyway)
I break headsets all the time, so I get the set at best buy with the 2 year warranty on it. I've replaced it so much that the people at Best Buy say things to me now. "Wow, you need a new headset often" "Didn't I see you in here a month ago?" Heh.