UW prioritizing admitting students whose last institution was a Washington state community college. Last year I read in the Seattle Times about a girl who applied as a freshman and was transferring from another 4-year institution and was frustrated she was not admitted... only she was transferring from Columbia University with a 3.6 GPA... She had to attend a community college for a year and then applied.
As other people have said, it's doubtful the prestige of your current school would be taken into account. If there is a way you could enroll at a community college, then do it. UW also takes into account a personal need to attend the UW (like the only school with a specific program, or needing to stay in the area, etc) and your financial need would be a nice way to incorporate that in.
So basically, coming from a community college, finishing all your pre-req's will put you ahead of 4 year applicants.