Depending on how quickly you want to have her status resolved, since she's going to have to go back to get the proper visa anyway and being able to work is important to her you probably want to look at getting married in the US.
In most states you can apply for your marriage license & get married the same day (California & Nevada Spring to mind).You can find each states requirements for a license here:
http://marriage.about.com/cs/marriagelicenses/a/usmarlaws.htm fees will vary from place to place but the above site is a good place to start.
Then she would apply for a spouse visa currently $1030 but that will go up in November. The visa is good for 27 months and she can work immediately upon arrival back in the UK on the spouse visa.
Marriage in the UK:
She would need a Fiance(e) visa currently $1030 and that will go up in November with the Fiance(e) visa she can remain in the UK after marriage but would need to apply for a FLR(M) in order to stay longer than 6 months, she would also not be allowed to work until she had the FLR(M) and the ID card.
OR
A Marriage Visitor Visa - which is about $120ish and it is valid for 6 months, she would not be able to work and must get married in the UK during the 6 months of the visa and RETURN to the US in order to get her Spouse visa (currenly $1030).
So if you want to marry in the UK it will take 2 visas minimum and at least 1 trip back to the US to get the initial visa, in the case of the Marriage Visit visa it's 2 trips back to the US.
As far as the actual marriage in the UK you would need to contact your local Registry Office for information & cost on a UK marriage as there are notice & residence requirements before you can marry.