Leigh, Chalkwell and the Leigh end of Westcliff are very nice to live in - we lived there, near Chalkwell Park for 14 years. If you go north of the London Road/A13, house prices drop.
All three dses went to Chalkwell Hall School, which had a very good reputation then - not sure now, as we moved away some 4 years ago, and my youngest is now 15. Leigh North Street always had a good reputation too. Darlinghurst was improving a lot when we were there, and had a really good 'feel' when we went round it.
St Michael and All Angels church, on Leigh Road, had a good pre-school, as did Leigh Road Baptist Church, which also had a friendly toddler group - I say 'had' not 'has' simply because I don't have up to date information on them, not because they aren't good any more.
When the dses were little, and I was working, they went to Little Treasures day nursery in Westcliff, and we were always very happy with the care that they got there. LT did before and after school care, with drop-offs at some local schools (including Chalkwell Hall, iirc), so can carry on providing care once children are of school age.
I had a friend who's daughter went to West Leigh school, and they found it pushy and not very good with children who weren't round pegs in round holes, if you know what I mean - though again, that might have changed in recent years.
When it comes to senior schools, Southend still offers selective education at Southend High Schools for Boys and for Girls, and Westcliff High Schools for Boys and for Girls (four separate schools, iyswim). Ds1 went to Westcliff High, and ds2 to Southend High, and a friend's dd went to Southend High for Girls, and we were very impressed with the quality of the education they were getting. Belfairs High has also improved a lot, as far as I know, and is doing a lot of building so has good facilities.
I loved living in Southend - I found it to be a very friendly place, and I made a circle of friends who were, and still are, very dear to me, even though I know live 450 miles away.
Good luck with your move.