LOL at 'top right corner' -- it is really lovely up there though.
Snow gets old really really fast, and also dirty. And with the usual 2 weeks maximum vacation time per year, you won't have much leisure time to enjoy it together.
You will need to research minutely the kind of schools that are available and pick a school first, then find a house in the district if you choose public schools (you will have a child in elementary, middle and high school judging by the ages, so you'll be looking at 3 separate schools, probably 2 separate districts; middle and elementary sometimes fall under the same administrative area).
You would also want to look into US universities and the cost thereof, and what sort of financial aid might be available for your DCs (none if not permanent resident aliens or citizens afaik)or whether you could afford to pay the full tuition whack -- so UK universities may be your only option, for your oldest at least, depending on his citizenship status.
Your oldest might have trouble with the US education system so close to crunch time where university entrance goes. College-bound American students usually do 5 or 6 subjects every year for the 4 years of high school. They need to do four years of maths, English, a foreign language, history/ humanities, and lab sciences, in addition to electives such as music or art, and get superior grades in each subject if they're aiming for a selective university. So a bit different from the UK.
There are excellent public high schools in many affluent suburban areas, and magnet schools in many big cities, where enrollment is very competitive. Public schools are free and completely secular. Private schools tend to be very expensive -- DD1 turned up her nose at one where she got a scholarship and the tuition would still have set us back about $10,000 a year (dodged a bullet there, thank you DD1).
Healthcare -- US companies sometimes use a solid healthcare package as a way to attract top talent, so this is something you may be able to negotiate depending on the company. You will have to have all the Is dotted and the Ts crossed on the health insurance before you leave the UK because you don't want to end up empty handed when you get there because of pre-existing conditions, etc.
Above all, I hope your DH researches the company that has made him an offer and is sure of its prospects. You don't want to be stranded -- US employment law offers very little for terminated employees and you may find your immigration status requires employment or sponsorship by an employer, or you could become illegal literally overnight.
Another important thing to look at is your relationship with your DH, and how much 'togetherness' you think the relationship can absorb without strains appearing. Right now you have a part time job, and you get out and meet people, you have your familiar busyness to occupy you. Moving to the US will circumscribe your world considerably. If the thought of constant cozy domestication sounds good to you, and you think you could use a lot more of your DH's company than you might have now, and far less of the company of your friends and relatives, then it might work out well. When you strike out to another country where you know very few people you are opting for a degree of social isolation, and a very unitary family existence, that can come as a bit of a shock. People in the US tend to stick with their own families and circles of friends while friendly on the surface, and while you may be a popular novelty for a bit, it takes longer to really establish a social network there than you might expect.