Which 3 miles on E.C.R. do you ride? In a lot of areas there are much nicer parallel routes. I commute from Downtown San Jose to Sunnyvale. Much of my route runs parallel to El Camino Real.

My opinion is that for 3 miles, you can probably commute on most any bike you want. My wife rides a pink cruiser bike 2 miles to the library and it works fine for her.

A few things that you might want to think about:
One really nice thing about the bay area is that you can take your bike on any of the public transit modes - light rail, caltrain, bus etc - but in some cases it will involve lifting your bike, and it looks like you may not be the beefiest of men, so a really heavy bike may not be the best option.

As far as local clubs for recreational rides, I like ACTC.ORG - they have organized rides for everything from a fast double century or long tour to a leisurely ride to a place known for it's pancakes.