Another very happy Raynes Park resident here! And we're also sending our child to the Rowans :)
I occasionally need the district line for work (I normally get the mainline into Waterloo), and when I do it's one stop - three minutes - to Wimbledon and then change. And the trains are frequent. We live just 2 mins' walk from the station. We rely on on-street parking as we don't have a drive, but it's almost never been an issue in the nearly ten years we've lived here.
The local area has decent shops and cafes, and you're a short hop to Wimbledon village or Wimbledon town centre if you're after more. At the weekends we can walk up the hill to the common, visit the pub and generally enjoy the combo of urban and country living the area provides. And yes, there is plane noise, but nowhere near as bad as Richmond! (Believe me - I wanted to live in Richmond, and my husband refused due to this point! He's very sensitive to noise and he doesn't find it a problem here.)
My recommendations:
www.rightmove.co.uk/properties/154940675
www.rightmove.co.uk/properties/155251433 (this is the "less desirable" side of the tracks but it's an easy enough walk to the station, and you certainly get more house for your money!)
But I see what you mean, not much on the market! Give it a month or two, I think people who plan to sell want to get through one last Christmas before having a clean up getting the house ready to sell in spring.