Wireless headset for sure
I attend a lot of webinars and don't like to be tethered to my computer (even though I'm generally an attentive attendee) so I much prefer a wireless headset (I have both kinds).
The Asus Travelite headset/mike I've had for a few years works very well. It connects with a USB and if I'm worried about whether the charge will hold for the call, I use an extender (it has a ridiculously short cord). The unit folds up into a nice round zippered case.
I agree with this reviewer who loves the headset, but complains about the poor quality manual--it took me awhile to figure out how everything works.