Where are you moving to?
Do you have a place to live? Do you have kids, if so what will you do with them over the summer? I assume that if you're moving in May they are probably not school age, but if they are you might want to organize some camps? Kids on the east coast generally do camp most of the summer.
In May the weather will probably be pretty warm, maybe with some cooler mornings and evenings, and it might get extremely hot before you get your shipped stuff delivered, so you will want spring/summer clothes.
In terms of your move, have you got forms to fill in for insurance of goods in transit? Are you organizing/paying for yourself, or are you being relocated by work? If someone is relocating you they should be being helpful about move arrangements. If you're paying for yourself give some thought to whether it might be cheaper to get rid of things and replace them when you get there, rather than paying to ship them.
Tell us more about your move, and I will probably come up with some more tips...
Oh, will you need a car when you get there? (You will, unless you are moving to NYC). Can you organize that in advance, maybe a month's rental while you look for one to buy? Usually renting from an airport is much more expensive than from anywhere else.
Bank accounts can be difficult for foreign nationals. You might want to look into that before you arrive, HSBC are good for portability so maybe talk to them before you go.