On the University point, I think I agree in theory, but not in practice. The percentage of their funding that's actually coming from the state has been dropping significantly over time. They're essentially private in everything but name and some slight discounts for in-state students. The demographics aren't that much different from similarly situated private universities. My sister went to a public school, which ended up costing more than my private school due to the scholarship I was able to get at the private university (I wasn't even that special, approximately 50% of the kids there got this scholarship).
If you go to UW, you have to apply to the CS program your freshman year. There's no guarantee you'll get in, due to space constraints. It's completely f'ed.