I am no expert on this; but I had Group Health and felt satisfied. At the highest benefit level you need to be referred by your "gatekeeper" for specialist care, but I think they are fairly liberal about it.
I now have Regence Blue Shield. I changed because I want to go back to my former Doc, who is not on Group Health, but is on Blue Shield.
Don't know anything about Blue Cross.
If you go with one of these, check how large their provider networks are, and if they are handy to you, have your own doctor on them, etc.
I think both University Hospital and Swedish are excellent. University of course is a core teaching hospital, with all the pluses and minuses of that.
Ha