I suggest that you should visit the Accommodation section under the Classified tab on this site and you will find suitable flats/apartments to your budget.

Once you find the suitable flats/apartments, search for the location using Google map to find out the distance to your workplace including the grocery shops and schools (maybe)... the rest would be easy for you to move around. The farther you live from west bay the cheaper the price is but you get a great value flat or even a villa for your budget.

You can get a fully furnished apartment either with your budget which also includes great facilities for your family. Think about the play area for your child as well.

Good luck!