I can't imagine adding Paddington into the mix. "It looks more complex" - well that's because it is. Lots of extra changes, lots of extra cost - and in the real world a time saving of a few minutes. For this journey I would never recommend it.
At the time you're leaving LCY, the DLR trains will be operating every four minutes. The destinations will alternate - one to Bank (in which case - change at Canning Town, down the escalator to the Jubilee) and the next one to Stratford not-International. If you get on the Stratford train - don't change at Canning Town (because it's a bit of a hike from those platforms) but instead go to West Ham and grab the District Line there. This looks longer but the end to end time difference is very marginal.
In terms of your original question, I prefer Barons Court, and find the front of the platform gives best chance of finding some room. As noted, in poor weather it's a bit exposed, so in that case Hammersmith might be better.