Congratulations on your upcoming nuptials!

As to the paperwork side, each US state has different standards for marriage so you will need to make sure you conform to their requirements. Where would you get married? If you need some time to marry, you may want to apply for a K-1 Visa - for Fiancé(e)s of U.S. Citizens (http://london.usembassy.gov/immigrant-visas/fiance.html)

You must:
one party is a U.S. Citizen;
both parties are legally free to marry; and
the marriage will take place within 90 days of the fiancé(e) entering the United States on the fiancé(e) visa.

As fas the spousal visa for the UK, a great place to start is with the Guide to London that has information on visas in the UK. There is also a FAQ section that addresses the UK Marriage Visa, or you can also consult the Obtaining a Visa to Live, Study and Work: the United Kingdom.

So, lot of resources

Basic Requirements:

Answering some of your specific questions:
Once the visa is obtained, (if the marriage is less than 4 years old) there will be given a 2 year visa to live and work in the UK or or (if Applicants who have been married and lived together for 4 years or more) they may be granted Indefinite Leave to Remain.

Processing times vary, but http://www.ukba.homeoffice.gov.uk/visas ... utside-uk/ provides the most up-to-date info. The standard is:
decide 95% of postal applications within six months; and
decide 90% of applications made in person at a public enquiry office within 24 hours.

Best advice is to do your research and network with other expats have been through the process in the forum, through the network (once you've posted a few times) or through expat blogs in the UK. Make sure to report back with questions and tips as you go along. Good luck!