Thetrainline.com always allows loads of time to cross London mainly because on bad days it can take that long. if they book you onto a connecting train and you miss it, you're completely stuck and would moan at them. If you get to the second station early, you can just hang around and wait and then get on the train you're booked on.
If you've got a lot of luggage then a taxi would be simplest. However at peak times it can take a while to get to the front of the taxi queue.
In terms of Underground, Jubilee LIne to Stratford and then change to the mainline would be simplest as there are lifts down to the Jubilee Line from Waterloo. Waterloo and City and then Central would be a pain with luggage as you'd have to go up and down several sets of stairs.
Buses - the times they take is very dependent on the traffic. I did Waterloo to Liverpool Street in 10 minutes one Sunday morning but it regularly takes 45 minutes or more at peak times.