>>983314if you get a front rack, too, then I'd recommend getting a wheel stabilizer as well. they're cheap and the stability they give a loaded front-end is profound.
for both front and rear, mount panniers as low as you can. the low center of gravity is a boon.
>>984214this. something slick-ish and probably as wide as you can fit thru your fork
>>987235totally this. I've also got a waterproof jacket and widebrim rainhat rolled up into my bike EDC so it's no big deal if I get out of the store and it's raining, my trip isn't ruined.
my EDC is in a wire basket with the little toolkit, pump, bungees, raingear, and lock in it, and the front light is strapped to it. when I lock up, I remove the basket and carry it around my destination; there's nothing on my bike to be stolen. there's still room for small purchases in the basket, too.
A messenger bag or backpack is a more familiar option but riding with stuff on your back gets old and your back gets all sweaty.
my current bike I built up as a car-less person specifically to be a city commuter bike. welcome brother!