I prefer open top folding grocery panniers. Easier to fit odd sized or oversized bags and parcels. If it rains I can cover the tops with a spare grocery bag, although I usually carry an empty yard/leaf size and strength bag for emergencies and to pick up trash or stray clothes for a donation box (I'm always surprised by how many serviceable clothes I find ditched along my rural rides, when there's usually a donation box only a few miles away). A cargo net and bungee cords keep things in place. I use the Nashbar Townie panniers, but Bushwhacker, JandD and a couple other makers all offer open top folding panniers.

I also have a plastic milk crate for the rear rack but don't often need it. And an large soft sided rolling picnic/beverage cooler that fits atop the rear rack -- it's waterproof and insulated, good for keeping cold stuff cold, or toting parcels to the post office or UPS/FedEx on rainy days. I rig 'em to the rear rack with heavy duty zip ties, bungee cords, nylon web cinch straps, whatever's handy.