I spend many hours running GoToMeeting classes online. I use the Logitech H360, and it does very well. It's a corded, behind the head outfit.
If you sit close to your wireless router, you probably will get interference with a Bluetooth connection.
With a good headset, and with good internet, you can have very high quality audio online. If your internet is not a "business grade" line, you'll experience times when your audio will just stall for a second or two, and that is very annoying. That's latency in the system. The cheap way to check it out is to use Skype for a few hours at peak traffic times. It will even let you record your voice and listen to it to check our outgoing audio quality.
I use Google Voice a lot. It's free outgoing calls, but won't work satisfactorily for most people for incoming.
