I think the question is "where to start".
1. Start with 'get a cross border tax adviser' (like me and others on this forum) and I apologise if you think that I'm not telling you about something simple enough that you could do yourself. I'm not. However, if you absolutely must do it yourself:-
2. Analyse the tax position in the UK and US if you ask for a secondment, as per the link I gave you.
3. Add in whether they'll support travel expenses, housing, set up costs, and the taxation on that
4. Add in the loss/gain of social security benefits.
5. Add in the change of cost of living, schooling, housing.
6. Consider tax on housing (gains)
7. Consider any loss / gain of pension/401k/stock option benefits
8. Repeat above for (b) if you ask them to start an office; for (c) if you contract as a self employed person, for (d) if you contract as a company.
The best position for you might be initially a secondment with travel and subsistence expenses, housing supplied, travel costs for family, education costs and anything else you can get on pension and stock options. After two years, you'll have to reconsider anyway.
Commonly, advisers like me talk it over with the company HR team to see what's best for both sides.