Sandown Park is virtually next to Esher station, there used to be
direct access to the course from the station at one time. It is a short
distance from Esher town centre however.
Depends on the time of day you wish to travel. If it is in the rush
hour the train is a better bet as the traffic around
Richmond/Kingston/Esher is chaotic and the schools are back next week.
buses are frequently very late running.
As Richmond tube and railway station are the same place. I would
suggest using NR Richmond-Clapham Junction then take a train to Esher.

Neill