Although others will tell you differently, I prefer having a cycling specific, fully water repellent rain jacket, with pit zips. Yes, you will heat up wearing a water repellent jacket, but if you are doing a charity ride in the rain, what would you prefer... heating up a bit or hypothermia? The pit zips allow you to cool yourself somewhat.
You can get a helmet cover that goes over your helmet that is waterproof, which works better in really pouring rain. I have several head covers for warmth that go under your helmet, but none of them would keep the rain out.
Wool socks (you can get thin cycling specific wool socks for warmer weather) and toe covers if it's like in the 50s and raining. Dressing in layers for days like this helps, particularly, a merino wool base layer.
You need to be wearing clear cycling sunglasses to keep the water out of your eyes.
Shivering involuntarily for 30 minutes is serious stuff.