The best Underground route is Victoria Line from St.P/KX to Oxford Circus and change to Bakerloo for Waterloo. It is a very easy change, about 40 yards on the flat. Nonetheless, if you have suitcases, I would simply get a taxi, much more expensive, but infinitely more relaxing, and should not take too much longer. There are usually oodles of taxis at St. P.
If the Eurostar is on time, you should get the 2.05 without anxiety. If you want time for a snack, book the 2.35. There is no catering on the train.