I want to ship a suitcase from London, UK to San Jose, California, USA?

Using a travel agent to ship a suitcase when time is not important will be a very expensive option. If you know anyone going on that route who won't be using their allotted luggage space, send it with them. Otherwise, just ship it via traditional mail carrier or UPS/FedEx/DHL. I would highly recommend that if you do ship it via some sort of carrier, pack it in a box instead of a suitcase for weight purposes.