You have a few options:
You can get get married outside of the UK - that would mean then applying for a spousal visa, which you would enter the UK on. That lasts two years (you can't claim any benefits), and then you can apply for indefinite leave to remain. After you've had ILR for one year, you can apply for British citizenship if you like.
You can come to the UK on a fiancee visa. You have to get married in the UK within six months of arriving and cannot work in that time. Once married, you get your two year spousal visa (can't claim benefits) and then ILR as above.
You could come as a student. You would have to pay international fees and could only work 20 hours/week during term time and full time during holidays. You couldn't claim any benefits.
You could come on a work permit. If you're not what the UK would consider a high Band 6 or Band 7, you wouldn't be considered in a shortage position and therefore would be unable to get a work permit or residency visa on that basis.
As far as the US to UK immigration goes, I highly advise you to join
www.americanexpats.co.uk . However, there's not a lot of nurses on that board, so it'd be best used for immigration queries to the UK and All Nurses used for specific nursing queries.
(I realise the thread is old but thought it was worth putting the information out there.)