Proper mudguards, walking shoes, if you're bothered about road spray then hikers gaiters can help keep the lower legs presentable.
Soft-shell tops are surprisingly good for showers and short sharp heavier bursts of rain and none of the boil in the bag problems of even lightweight or supposedly breathable waterproof jackets.
There is no worse cycling feeling than putting your feet back into damp socks, a spare pair is a godsend.
Also, if you don't anyway, put a pair of latex gloves in you repair kit, if you do happen to get a puncture or mechanical in the cold and wet, they make a heck of a difference to keeping some feeling in your fingertips.
A tea towel or one of the travel miceofibre ones packs nice and small and is good enough to dry you off sufficiently after a proper soaking if you are going on elsewhere and not changing just yet or somewhere with poor facilities.
Avoid puddles and wet gutters (avoid gutters full stop) never put your wheels into anything you can't see clearly through. Wet metalwork and paint on the road is far more slippery than the rest of the road surface.
It is surprisingly rare to get caught in proper rain that needs it's own accessories though, even in supposedly rainy Manchester, it's a rare treat.
As for luggage, I always spray my bags.with a waterproofing spray just to be belt and braces but generally if it claims to be waterproof it usually is for normal bad weather. If you're worried or it really is blatting it down, put your books etc into a plastic bag first then even if you do get leakage then the contents are safe.