A good few properties in your price range in Chessington atm
Trains half hourly to Waterloo from Chessington north or south or you can get 71 bus to surbiton for more frequent trains to other London stations
www.rightmove.co.uk/property-for-sale/property-85318619.html
If your budget can stretch slightly over 300k - this style of maisonette around garrison lane area (but go for the quieter side roads like this one) has huge rooms, own decent sized back garden and front garden. Short walk to station and on bus route. freehold is Kingston council
www.rightmove.co.uk/property-for-sale/property-88172066.html
Local estate agent told me lower end properties are more difficult to sell atm as new tax laws have put off investment/rental buyers and first time buyers are going straight for family sized properties - using inherited money As so difficult to save a deposit . so you might have room to negotiate.