Hi - absolutely right those are the three. Depending on your length of stay, finance and interests, they vary a bit. For all of them, check the lock can take 60', via email
You will need the tide to enter any of them. St K has a waiting pontoon which is fine (though don't park where the Thames catamaran
stops). The Limehouse one is a nightmare - you're better jilling about in the river. I've never been into South Dock
in a boat.
St K's will accept winterers on foreign flagged vessels but will not take your post. Limehouse are more relaxed, and has the huge advantage of the Cruising Association HQ (yes I'm a member) which offers a nice bar, teh library and various boaty activities. It's slightly further east than St Katherine's but the Docklands Light Rail will get you into London pretty fast. South Bank is fine from my on-foot visits but is slightly further on public transport. (I am talking about 10 minutes difference here, mind you!)
You could go up the London River (known to furriners as the Thames), turn into St K (the easiest to get into) and then explore to see what you prefer. Do not assume tey will open Tower Bridge for you - and there's nowhere for a yacht on the other side!
Send me a PM if you're around for a while!