Trains on both routes are every 30 minutes.
St James' Park is the tube station to use for Paddington- 8 stops on the Circle line
Green Park is the station to use for Waterloo- 2 stops southbound on the Jubilee line.
To me Waterloo is the closer and the easier as there is no change, BUT it is an uphill walk from Riverside Station to the station, however as the name suggests it is closer to the boats.
Central Station is more or less flat to the Castle, but it would be uphill after the boat!
To me there is nothing in it, route or time wise. It is personal preference. My preference will always be Riverside (from Waterloo), the overwhelming preference of the forum is Central (from Paddington).
On the Riverside route you can also take a District line train westbound to Richmond, and join the Riverside line train there;
or a Victoria line train from Green Park to Vauxhall (3 stops), and join the Windsor bound train there