Be advised that Caltrain is having money problems and plans to drastically reduce their service this summer, so if you ever need to commute after 8:30 AM or stay past 7 PM you might be screwed. That's a very long bus ride, or a high cab fare.
I stayed in motels as I got to know the area and decided where I wanted to commit to staying. Some offer weekly rates that are competitive with local rents. Sequoia Inn was nice, and it's in Redwood City: