My bike is a Surly Ogre; I got this Topeak rear rack with like a rail in the middle of it and a trunk bag with fold out side panniers. It was too small for groceries (unless I just bought a few items) but perfect for library stuff and vegetables from the farmer's market; I ride to town as much as I can and that seems to be what I carry the most. I was about to order some "grocery bag panniers" (banjo brothers brand) when I got the word from my mother that my sister was destitute. I may still order some.
A trailer would definitely be best for carrying stuff (how many cases of beer can one fit??) but I don't have a good place to keep one currently...