We moved here from the UK 8 years ago. It took 3.5 years to get a green card, and I was not allowed to work until that came through. Not sure how long yours will take, but I'd base your planning on that. At least that way you can keep current in the UK whilst earning and building hours whilst going through the process of getting the card. And, while all that is going on, you can get your FAA ATP written out of the way, then do a condensed course for the checkride once you get here.
Also location is very significant - if you are moving to the north of North Dakota or the south of southern Alabama, there won't be so many jobs. If you are moving to Chicago or Miami or San Francisco or New York or Detroit, so long as you are willing to try different parts of aviation - instructing, charter, corporate, etc as well as airline flying, you would have a better chance of finding work. Have a look at propilotworld.com - its a useful forum to build contacts and observe comments on the health or otherwise of the aviation industry.
Good luck - hope all goes well with the wedding too.