I am not an expert on this tho I have done what you want to do and gotten the green card from the UK.
Firstly, I assume you want advice from UK citizens who are US residents rather than UK residents.
As I understand it (and I could be wrong) it is nigh on impossible for UK citizens to get green cards straight away without getting one of thouse exemptions for making a substantial investment in the US ($2m+) - which it doesn't sound like you are suggesting you can do.
If you have an Irish passport, apply in the greencard lottery and you will have a good chance (50%?) but less than 5% if you are a UK citizen. I believe the situation is driven by a UK limit to reduce 'brain drain' emmigration - the UK limits US entrants to make sure that the US retaliates to limit UK immigrants (sounds kinda wacked but that is what I was told). I know that I have had US friends kicked out of the UK for coming over for extended training programs.
So - to cut a long story short - if you are transferring with a company and you have over 1 year of tenure before you come then you can come on an L1 visa. If you can get your company to classify you as 'management' then you can get an L1A - from which, a green card is (was) a shoe-in in less than a year with about moderate cash/legal effort. L1B's take about 3 years and more cash and legal effort to convert since your company does less to prove how valuable you are to them in the first place (the INS takes more on trust from your company with those). If you have less than 1 year of tenure then you get an H1 visa which again takes 3 years or so to 'upgrade' but needs even more involvement from your company to prove your value to the USA as a permanent resident. There are lesser visas and more variations on the ones I mentioned but all my expat friends have used the above methods to get over here!
Basically, if your current or future employer will not 'import' you then you are probably a long long long way from a green card
That is the limit of my knowledge/misinformation so others will have to add or amend but good luck!
The Cap'n