We have twin boys (16 mths old) and a 4 year old - we use a 'Maclaren' double stroller (where they sit side by side) and have a 'Buggy Board' attached for when our 4 year old is tired. It works very well, but as we now live in hilly Yorkshire, my wife and I have Popeye style upper arms!!!
As for whether to buy a stroller here or not, I'd guess it'd be cheaper to buy in the US, but it may be a hassle to bring it over. We have always found Mothercare (specialist baby store) and John Lewis (department store) to be good places to test out strollers as they display a wide range, but as for actually buying the stroller, go to a local independent store, where they can order it for you and you will get much better service and often a cheaper price. Our local store actually lent us a stroller for free while the old one was being repaired - the big stores would NEVER do that!
Getting a double stroller onto buses/trains can be a pain, as not all vehicles are properly equipped and are often overcrowded. We managed in the London suburbs for 1 year with a young baby and no car, but I must say that life became very much easier with a car. See how it goes and try to live within walking distance of shops/services if you don't want to rely on a car.
Good luck with the move and the second baby!