I can put a lunch packed into the 4x6" or 5x7" ziplock boxes (or similar) in my pannier along with clothes. Clothes get rolled up (and loaded in a plastic slightly-larger-than-grocery bag) on one end of the pannier, lunch goes in the bottom on the other end, pocket contents in a quart bag, belt, and cell phone go on top of lunch and stabilize the clothes.

If I'm not hauling in fruit for snacks, a Kleen Kanteen of coffee stand upright in the other pannier beside my shoes. Hasn't leaked yet.

Panniers are Ortlieb Sports Packers, FWIW.