I would like to use a wireless headset to create documents with speech recognition software.
I understand bluetooth communicates with a phone. What equipment should I use for the computer mic jack only ?

A lot of wireless headsets I've seen or read about, all seem to use bluetooth. The prices are quite reasonable now and will normally include a bluetooth receiver dongle. The bonus is, is that your PC is now bluetooth equipped. :) The Bluetooth protocol allows up to 7 devices, so you could have a bluetooth equipped mobile phone, or a keyboard, or a mouse, all connected.