You can get married in the UK on a Marriage Visit Visa (this is the option I took). You would have to return to the US to apply for the Spousal Visa then before you could return to the UK to settle.
Info on Marriage Visit Visa here:
http://www.ukvisas.gov.uk/en/howtoapply/infs/inf2visitors#9248746Marriage Visit Visa: £67
Spousal Visa: £585
plus cost of travel, etc.
We chose to get married in the UK because my husband was short on vacation time from visiting me in the US so much already. We were married at the Coventry Registry Office
http://www.coventry.gov.uk/ccm/navigation/council--government-and-democracy/council/register-office/Registry office ceremony is the equivalen of a courthouse ceremony in the US, however so many of the registry offices are in historic buildings. And we'll still have a ceremony (however we won't be signing another licence) in the US next summer for my family that wasn't able to attend the one in the UK.
Really it's up to you and your fiancee where you want to get married and weigh your options- family, venues, cost, etc. Don't stress to much about trying to make everyone happy- you need to do what will make you and your fiancee happy. We had a small ceremony at the registry office, and a backyard reception (we went to the pub that was across the street from the registry office before the reception also). Everything was very DIY- we made most of the food for the reception ourselves and I think all in all, we spent around $1500 for everything including the ceremony fees, my dress, flowers, food, drinks, etc. The great thing about getting married in the UK I will add is the amazing honeymoon options afterwards! It's fairly inexpensive to get to the continent and honeymoon in Paris, Rome, etc. (That's what we did- Paris- soooo romantic).
Best of luck and remember, you need to make yourselves happy first!!!