Really there's only a handful of visa routes to go through if you're looking to move to the US on a permanent basis. Hopefully this will make it easy to rule a few out quickly and then you'll know which ones to look into more closely.
1. The Green Card lottery - designed to make the US culture more diverse by bringing in more citizens from countries that don't have much of an immigrant population in the US already.
If you're a British citizen by birth you cannot be entered into the lottery. If you are a citizen from one of the countries on the lottery list then you can, but it's still pure chance whether you'll be selected and it's not an instant move if you are - you are still subject to the process of getting your documents through your local embassy, which can takes 1-6 years.
2. Business investors - If you intend to start a commercial enterprise by investing $1000000 and/or creating jobs for at least 10 United States Citizens (USCs) then you can come in as an investor. Not sure what the rules are about you staying if your enterprise fails though.
3. Somebody with exceptional skills - top class surgeons, ground breaking scientists, etc, can get entry riding on their CV. But you really do have to be the best in your field with some sort of national or international acclaim.
4. Sponsored by a Senator - usually only used by government or business officials when they've accidentally let their current work authorisation run out and are suddenly subject to deportation. You'll need to know people in high places.
(PROBABLY NONE OF THESE SO FAR, RIGHT?)
Here are the more commonly used routes...
5. H1 visa (skilled workers) - You will need a bachelors degree or higher, and sponsorship from an American employer. Getting sponsorship can be a bit of a catch 22 as a lot of American companies that say they are are willing to hire foreigners want them to already have work authorisation. But if you can get an internal transfer in a company with UK & US offices it's not so difficult. There are a limited number of H1 visas made available in April each year, first come first served, so you may find that come June there are none left and you'll have to wait until the next year.
6. H1 visa (unskilled workers) - You can still apply for a work visa without a degree, there are only certain careers that they have a shortage for though and the demand is very high.
H1 visas are processed to start working in October of the current year, they last three years initially and can be extended for an extra year up to three times. If you intend to live in the US permanently you need to apply for permanent residency shortly after arrival as the process can take up to 6 years, if it isn't complete before your visa expires you'll have to leave the USA and finish your application from abroad. The unskilled route has a waiting list that takes 5-15 years to get to the front of (before you even start the application process) it's easier just to get a degree. If you are going to foot the bill for an H1 visa, consider putting away $4000.
7. K visas - If you marry a USC you have two options: marry somewhere other than the United States and apply for permanent residency from abroad (you will have to stay in your home country until the application is approved, but once you arrive in the US everything is pretty much sorted) ... or apply for a fiance/e visa - which allowed you to enter the US and get married there (after which you will have to apply for permanent residency). The application process takes about 8-12 months to get there, with further paperwork to maintain lawful resident status at 2 and 10 years after marriage. You'll need about $2000 to file the paperwork for a K visa, but you can split this cost with your fiance.
And lastly:
8. something else - there are some other ways of going about immigration to the USA, but the border officials don't really like them as it usually involves entering on a visa that was designed without immigration intent, which suggests you lied in your original reasons for entering the US.