Myself and my wife moved from inner London to Great Notley in 1999; I'm originally from a small town outside of Manchester and she's from Ireland, so neither of us really liked living in London and wanted to have a bit of the "country".
We came across Great Notley pretty much by accident and fell in love with it straight away. Great Notley village itself (which is where we are) is great...it's self contained in so much as people even liken it to The Truman Show movie. We have a Tesco (for better or worse, you decide), 'village' pub, GP surgery, vet, fish & chip shop, Co-Op, new Chinese take-away and lots and lots of space. It's only a few minutes walk from the Discovery Centre (Google it) and Notley Country Park. Braintree itself is pretty provincial (again, for better or worse) and it does have its fair share of what you'd probably call stereo-typical Essex people. We don't really have that much cause to go into Braintree itself and Chelmsford is only 15 minutes drive away (Stansted Airport is only 15 minutes away too).
Our little girl is only 22mths so I can't vouch for the local schools first hand but there are some very good ones (Google Felsted High) in and near the surrounding villages. Our little one goes to the Just Learning (recently changed to Busy Bees) day nursery which is actually on Great Notley Village and they've just received an 'Outstanding' OFSTED report. As far as crime, our only experience of anything like this since we've been living here was a couple of months ago when somebody keyed 3 cars in our street...I'd say that's not bad if it's the only thing in 14 years.
It's not what most people picture as Essex...there are wide open spaces and it's a really beautiful place. It's also well placed for lots of things such as the M11, the airport, Chelmsford, etc. Many people on Notley Village move and actually just buy another house on the village, it really is that nice a place to be...and when you're on Notley, it kind of feels that you're away from the world and in your own little country village. I saw this via a tweet and have just registered simply to reply to your post.
I'm afraid that I can't tell you anything about Chelmer Village but if there's anything else you'd like to ask me, please let me know.