Bags
Few bicycle panniers are truly waterproof. So we suggest you pack your belongings in plastic bags. Use several small bags rather than one big one: it takes up less space and is more practical.
Bring dry clothes (t-shirt, socks, fleece) to change into at dinner. You won't regret it!
Clothing
Equip yourself with a good two-part raincoat (jacket and pants). It should be lightweight and equipped with ventilation points. Gore-Tex products are excellent - this fabric breathes while providing effective protection from the rain - but are rather expensive. Avoid ponchos or fireman's raincoats! The former offer far too much wind resistance, while the latter will make you sweat so much you'll be as soaked as if you hadn't worn a raincoat.
For your feet, there are overshoes available from bike shops. Alternatively, wear wool (or fleece) socks in your shoes. Your feet will get wet, but at least they'll stay warm. Avoid cotton socks and makeshift «wrap-your-feet-in-grocery-bags» solutions, as your feet will tend to slip off the pedals.
Finally, don't wait for a deluge before putting on your rain gear. It only takes a few minutes to avoid getting soaked and freezing all day.