It is tricky OP isn't it, to find the right neighbourhood, especially when you are not here.
I think firstly you are restricted by your 500k budget (I don't necessarily say this as a bad thing, because it helps you narrow down to a few places that still has good value properties, rather than being confronted with alot of choice, like that lady who was on this forum a while ago with a £3m budget, she could practically live anywhere and had a very difficult time deciding)
Then it's the quality of schooling, as someone else said, if your son is 3 or 4, you have many years before you need to start thinking of secondary schools, and unfortunately no one can plan 7 years ahead, and lots of changes could occur in the interim to the local school scene. I would just focus on the primaries for now.
Next you need to decide if you want the urban or suburban feel, places such as Beckenham, Petts Wood, Chislehurst I would say are more suburban, quieter, greener, bigger houses (maybe more 30s than Victorian/Edwardian), whereas all these "villages" around Lewisham have a more urban feel (busier, noisier, more culturally and racially diverse). Each to their own and you've really got to decide what your personal preference is.
Regarding your husband's and your ethnicities, you will find that the suburbs may be a bit more racially homogeneous, but I would be very surprised if you would experience any sort of discrimination, as London as a whole is one of the most tolerant cities in the world.
Lastly don't forget transport, London doesn't have the most efficient tube/rail networks, with signal failures, development works, and strikes. Try and make your commute as simple as possible. Don't forget to factor in the waiting time as well as the travelling time, this is a good tip someone gave me when I was house hunting, it could take 25 min on the train from place x to central London, but that train may come once every 30 minutes, and this is important to bear in mind/research into.
Good luck!