If you get married in the UK, you'll need to go back to the US to apply for your fiancee' visa. Once you have that, you can come over for the marriage. You'll need a certificate of approval and will have to give notice, etc. (others will know more about that).
If you marry in the US, the UK fiance will not need a visa as you won't be living in the US after the wedding. You can apply for your spousal visa from the US after the wedding and can move to the UK and work straight away.
If you marry in a third country, you'll need to make sure that the wedding will be recognised as legal by the US/UK authorities.