If you are doing a return trip, then take the Amtrak from Seattle to Vancouver in the morning (it is not fast, particularly the last hour into Vancouver - the bus would be faster) and on your return take the Pacific Coach Lines bus to Victoria (awesome ferry ride). In June, the BC Ferries' service is hourly. From Victoria, you can take the Victoria Clipper to downtown Seattle - google for schedule and fares.
With all due respect, don't follow #2's suggestion of Sidney/Anacortes and/or Victoria/Port Angeles unless you have a car which, if you want to take the train, you probably don't have. Very convoluted way to get from there to here.
If you can only do it one way and you really want to do the water route, it is probably the more scenic. For speed, take the bus.