We used to live in Chalkwell - just down the road from Chalkwell Hall Schools, and the park, and we loved it there - easy access to the park and to public transport links into the town centre, shops and library within walking distance up the London Road, and my husband could walk down to Chalkwell Station in 10 minutes, to commute into London.
I found it to be a very friendly area - I made some wonderful friends who I am still in touch with, even though I now live in Scotland - and everyone was very open and welcoming.
There are good pre-schools in Leigh - St Michael and All Angels is one we used - ds2 and ds3 went there and were very happy, and also Leigh Road Baptist church, where ds1 went - they also have mums and toddler groups, and when we moved to Southend, that's where I made my first friend in the area. I would definitely recommend the Leigh-Chalkwell area, and the Chalkwell end of Westcliff.
It is a bit of a way off for you yet, but there are good schools in that area - we were very happy with Chalkwell Hall Schools, and have heard very good things about Leigh North Street school (it is a smaller school, and very popular indeed). West Leigh School has a good academic reputation, but when we were there, it was known as quite a pressured environment, and not so good at dealing with square pegs in round holes. Darlinghurst school didn't have as good a reputation as the others I have mentioned, but we did look round it at one point (we were thinking of moving ds3 because of bullying issues at Chalkwell, but these were resolved to our satisfaction, so didn't need to), and I felt it was a school with a lovely atmosphere and happy kids.
Senior school-wise - that area has Westcliff High Schools (Boys and Girls - separate schools) and Southend High for Boys - Southend High for Girls is over in Southchurch. All of these are selective (11+), and have very good reputations indeed - ds1 went to WHSB, ds2 and his best friend to SHSB, and a very close friend's dd to SHSG - and all did do well there.
If your child doesn't pass high enough in the 11+ for these schools, there's Belfairs High school - a comprehensive that was good when we were there, and improving - and was embarking on a lot of new building. Eastwood School is also very popular.
There seems to be a very clear divide in property prices north and south of the London Road - with houses definitely more expensive south of it.
I would also recommend renting for a while - that's what we did when we moved up to Scotland, though we had to rent in the right area for the senior school we wanted for ds1 and ds2, whereas you could rent anywhere in the Southend borough, and would still be able to check out other areas of the borough (houses, parks, schools etc) easily.