Relocating is easy if you have good support (ie money) from the employer. It can be quite hard as a DIY job, as there will be quite a lot of paperwork to be done before you can become a real person. New Jersey is quite a diverse place, so what it's like depends on where you are going to be living. There are lots of British Expats there, and it would be easy to connect with helpful people who can support you in the early months.
Schools officially start a year later than the UK, with many summer born boys being held back a further year. At 4, your DS will go into pre-school (ie nursery in Britspeak) - 3 or 4 half-days a week; pre-schools are always private. The quality of the schools depends on the area that you are living in, so one of your goals is to live in a good school district.
You can get all sorts of daycare, including daycare with pre-school and kindergarten programs. You are unlikely to be working in the US - a foreign spouse fits into very few visa categories that allow work.
NJ is one of the most expensive parts of the US. You would be able to get by on similar amounts of money to here, but if your really want to enjoy your experience, then you'd need a lot more. How long is a piece of string, basically.
My kids were almost 8, 6, almost 3 and 5 months when we left, and they were fine with the logistics of the move, making new friends etc. It quickly became "normal" for them. 4 years later, they were fine moving back too.
There's a lot more to think of, but of a very practical nature - where you are going to live, what kind of house, your visas, opening bank accounts etc. If the job works out, I suggest you join an expatriate site, such as Britnet , where you can get help from people who are going living it now.