If you really, really want lots of rail:

Piccadilly Line to Acton Town
District Line to Turnham Green
District Line to Richmond
Train to Clapham Junction
Train to Guildford

You could also change at Earls Court and West Brompton to take in some fine old tube stations and the London Overground.

Personally, if I didn't fancy the railair bus or Beeline Taxis, I'd get the bus to Feltham, then the train via Clapham Junction from there.