Personally I dislike umbrellas, as I'm of a height - 6'2"/187cm - where on rainy city streets I constantly have to dodge the ribs of other's umbrellas lest I lose an eye.
I have a waxed cotton hooded raincoat made by Filson (a model no longer offered since their latest revamp) which works surprisingly well, and breathes a bit better than synthetics. Found it new on a discount rack at an Army Surplus store here. Large enough to fit over another jacket if need be. I make a point every summer of taking a lazy hot Sunday to re-wax it and set it out in the sun for the day, adding more wax as the fabric soaks it up. Minor annual maintenance for something that's worked well for five or six years now.
As for shoes, I normally wear leather boots treated with Obenauf's. Work fine for most inclement weather. If a truly muddy day is on the horizon, I'll wear those "Maine Hunting Shoes" from L.L. Bean (which also get an annual treatment).