I grew up in Rayleigh and worked in Chelmsford, so have a little knowledge about both areas.
Rayleigh
The two secondary schools - Sweyne and FitzWimarc - are very good and the majority of residents speak very highly of them. I am a little biaised as I attended one of them. One of my children attended the grammar school in Westcliff, the other attended FitzWimarc. Both children did very well, with similar results at GCSE level, so it's probably more about their response/application to being educated and how well they adapt to criticism/praise from their teachers.
I'm not quite sure if it is correct that Wolsey Park falls within catchment to the Chelmsford grammar schools, but I acknowledge that my experience is from
a long time ago now. However, what definitely used to happen is that everyone who took the 11+ exam, were placed in order of how well they did. Generally the top 200 entrants (i.e. were placed from 1-200), were offered a place at any one of the local grammar schools. Anyone placed from 200 onwards were not offered a place. In Southend/Westcliff, there was definitely a 'catchment' area, whereby they did offer places to local children more favourably than those having to travel from other areas. The Chelmsford grammar schools are much more difficult to get into - they generally take the top tier of 11+ entrants. Of course, it may have changed in the last 15 years, but I really don't think living in Wolsey Park will give you an advantage.
There are plans to build more houses at the Lubbard Lodge farm area (other end of Rawreth Lane), so the roads which are busy now, will likely get busier.
Wolsey Park is a new estate on the edge of town. There is kind of a 'wavy' cut through from Rawreth Lane to Rayleigh Road and there have been complaints about cars cutting through, as well as the build quality of some of the properties there. There are also approximately 100 social housing properties, if that is something you weren't aware of. Honestly, with £600k to spend, I would choose somewhere else in Rayleigh. Arguably the best area of Rayleigh is Great Wheatley's but there are plenty of areas in Rayleigh that are very nice. I wouldn't consider Wolsey Park to be one of them.
Chelmsford
Definitely a little more diverse than Rayleigh, with a multi-cultural society. Don't rule out Rayleigh because it may be a little behind Chelmsford in that regard though. Both places welcome all nationalities and you will find many children at the schools from all areas of the world.
I don't know much about the local schools in Chelmsford unfortunately.
The grammar school (one boys one girls) have an excellent reputation, but they do pick the best of the bunch and consequently are very difficult to get into.
One area of Chelmsford to avoid would be Melbourne, but there are some very nice areas of Chelmsford, for example, Writtle. Lovely period properties and a green, with quaint shops etc., but not near the station. There are now two stations in Chelmsford. The one in the centre of town is close to the Moulsham area (a good area with period properties), and there is a new station at Beaulieu Park. There is also a park and ride bus service which would take you to the centre, which you might find easier for parking etc.