First, welcome to the Northwest. I would encourage you to consider several things; proximity to work, freeway, preferred type of entertainment and of course schools. I've attached a link I like that allows you to compare school ratings from district to district and even schools in one district to others in another.
I believe you'll find that the Bellevue, Lake Washington and Issaquah Districts are all very good, but depending on your kids specific needs you may find one district or school within each district may suit you best. There are gifted programs, foreign language, technology based, arts based options in the area and probably others I'm not mentioning.
Regarding availability; our inventory is low at most price points. What is available today, may be gone long before you're ready. Prices are seeing substantial increases over last year, in large part due to low inventory and more migration to the NW than away. Several builders have broken ground on new projects in the past several months, so I suspect they are betting on this continuing.
To answer your question more completely, here is what I'd suggest. Find a Broker out here that you are comfortable with that you can start a long term dialogue with. We practice Agency Law in Washington, which means that whoever you select will represent your needs first and keep your confidences, unless they are already contracted with the seller.
Your local agent can gather additional information about your family, your wants, needs and plans to advise you further. They can send you listings, preview some for you and of course prepare tours when you can come to visit.
I'm a Seattle area native and I've live in Sammamish since 1988. We've raised our boys in the Lake Washington School District and know it well. You'll have many of us that will be glad to help, so do some research on the Brokers who respond and pick one you like and can trust.
Welcome again to the area, we hope you love it as much as we do.