We bought all our white goods at ABC warehouse, Sears, and best buy. We found that we could usually haggle a bit on price. There are lots of decent discounts when you open a store card - usually a % off your purchase for the first month.
Are you buying a car outright or on finance? You may want to get your US credit history/ score and see what it is (if you've lived here before I assume you have one) and tidy up any inaccuracies. We moved here a couple of years ago and struggled to get finance with our limited credit history - your local credit union is probably the best bet.
Best buy are famous for terrible service with delivery, so take a pick up truck if you buy from them, we did. We got the best deal on fridges at Sears in the new year sale one year. Cars, it depends on what you need. I drive a Ford Taurus, nothing fancy, big trunk, room for three kids in the back seat with a bit of a squeeze with car seats. More than two or three kids I love the Toyota minivan. Where will you be moving to? Do you have jobs already, cause they seem pretty thin on the ground around here. Houses are cheap, the market seems to be picking up very slightly, in our area, there are not many for sale at all, unless you are looking for a foreclosure that needs a ton of work. I second the local credit union for banking, we love ours, no stupid fees for everything and fee free atm's.
I am moving back to my hometown of Birmingham, Alabama. Houses are quite cheap there and there are plenty on offer in the area I want to move to. No job as yet but have a few leads.
I never closed my account with a local credit union. My DM would pay money into the account for our birthdays and Christmas. It was always used for spending money when we went for a visit, but haven't had a credit card in the US in over 20 years. So I might have some credit history - not sure far back the credit organization hold their records.
I really would like an economical car. so suggestions welcomed. I don't need anything very big, will only have 1 DS living with me full time and one at university who will also need a car. Eldest DS staying in UK for university and no3 DS staying here to complete his GCSEs (both will be living with their father).