Fenders are a must, full coverage if possible. It's not so much the rain that falls down that gets you soaked, it's the water on the road that sprays up. Lights are essential if you're going to be riding after dark, and also help in rain or poor visibility, not so much so you can see, but so car drivers can see you.
I normally just wear an ordinary raincoat in wet weather. If the facilities are there it would be good to take a spare set of dry clothes to wear when you get there if it's very wet. Your feet will also get wet, so any shoes that keep the water out are good.
Other than that, you can get by with your normal clothing, underdressing slightly for the temperature as you will probably be warmer cycling than walking.