Someone will be along shortly with the details, but based on prior posts and the responses, you should really plan on going back to the UK at some point prior to moving to the US to live with your girlfriend. If you come over on a VWP, marry and then try to stay, it looks very bad.

Others can tell you whether your best option is to go for the fiancé visa - and then marry on your return trip - or to get married while you're in the US this time, return to the UK and then get your spousal visa. But making the trip back to sort out the proper paperwork can save you major hassles later on.
Cheers,
Bev