Tom's suggestion of a list of what you want would be of great use. You didn't mention the size of your garden. If your gardening is limited to containers or a small area, you may not want to order a large amount of soil or compost--unless you and a neighbor decide to share. If yes, there are several good sources, such as Cedar Grove Compost. The downside is the minimum amount you'd have to order to qualify for home delivery!
So, I'm going to assume your garden is more like the average small city lot with some vegetable or flower beds, interspersed with containers.
My go-to garden supply catalog, when I can't find a tool or gadget locally, is Gardener's Supply out of Vermont. Shipping charges are more than reasonable and the selection for the average home gardener is quite good. And, yes, you can order potting soil.
For greenhouse supplies, big and small, check out Charley's Greenhouse and Supplies in Mt. Vernon, WA. Even if you don't ever want a greenhouse, you can find other helpful tools and potting supplies.
If you're looking for plants, well there are so MANY small plant sources in Washington and Orgeon. Here are a few examples:
A&D Nursery for peonies, daylilies, and hostas. My favorite source for lilies is B&D Lilies near Pt. Townsend. Fancy Fronds has wonderful ferns and never fails to disappoint when you see their garden display at the Northwest Flower and Garden Show.
Speaking of the NW Flower and Garden Show, attending is a great opportunity to discover local growers and suppliers. The show is next month, February 8-12 at the downtown Seattle Convention Center. While tickets aren't cheap, once in the show you can attend free seminars, view the inspirational garden displays, talk to lots of experts, and shop.
Also, don't forget to view seed catalogs. I always have Territorial Seeds and Johnny's Seeds catalogs on hand for ordering and reference.
Well, I hope this is a useful beginning. Happy Gardening!