I commuted for years with the small front Ortleib panniers on LowRiders. (Climbing hills on fix gear with weight over the rear wheels sucks.)
Once a week, I brought in clothes for the week and brought home last week's. I would shop on the way home. (Really easy. Bring in the panniers and put them in the shopping cart. Have the cashier put my food back in the cart. Then I'd load the bags as I wanted, ride home, carry the bags into the kitchen and unload.).
I love that those panniers are really waterproof. Everything stays dry. Or, on farmer's market runs, I can roll them closed at 11 am and when I get home at 2:30 on a summer's day, my greens are still fresh. (And any produce residue wipes off and dries really easily. Major mess? They clean up like a dish.
Ben