Best to stay 3 weeks or more and get yourself resident: social security card, driver license, library card, bank account, etc. Card will probably arrive within 3 weeks -- but even if it doesn't, the stamp in your passport is good for up to 1 year.
It's okay returning to the UK to wait for your house to sell, but try to keep the time out under 6 months. All houses will sell -- you just have to price them correctly. BTW, by selling your house after you become PRs, you could open yourself up to US CGT liability.