Ours came from a private school so the class sizes and facilities were familiar, I think this helped. Bear in mind that your youngest won't enter kindergarten until the September of the year he turns 5. Most go to Pre-K beforehand but availability during the school year is tough as they're all private.
The curriculums are different, but not hugely so. Lots of American history obviously
which is an education for us too. I think the pressure here comes in middle school. It's nice to see the kids out of uniform, a lot more relaxed. This helped them settle too as they weren't overwhelmed by the schoolwork. The summer vacation is very long - 11 weeks! We did workbooks to keep their brains ticking over.
Honestly, the kids were great. We had no tears. They're very resilient and adaptable, they'll surprise you! We moved at Easter, and my eldest started about 4 weeks before the end of first grade. The teachers and kids were so incredibly friendly and welcoming, and still are
. They're used to people starting mid year as even if you move house locally, you can only go to the school assigned to your house. Such an easy system - we're trying to move back to the UK next summer and getting very stressed about schools!
As a pp noted, Greatschools.com has ratings of districts for you. Is it a temporary move? If not look at middle school results too. Some private schools aren't too expensive BUT they're unregulated so I wouldn't consider.
I can't comment much on CT or NJ. Greenwich is lovely but pricey. The commute from here is a pain - 45 minutes on a fast train and they're infrequent off peak so I wouldn't want to live much further away. We have friends who moved here from Hoboken (NJ) and Brooklyn because of the schools availability.