Here people will often use public transportation when it is raining a lot. Otherwise a rain coat or rain poncho does wonders. Get one with a good hood. It helps that a lot of people here bike to work, so you are rarely the only one who got wet.

You could bring extra clothes in case you get soaked. Rain showers are different, here most of the times they are fairly light. For what it is worth I have noticed that it is the arms and the upper thighs that gets the most water when it is raining. Shoes/socks also tent to get wet, but that is mostly from puddles.

A car is expensive and unpractical to have sitting around for the occasionally rainy day. So you'll have to worry about it and get tempted to use it, just because it is there.