Rack, definitely. It's more comfortable and efficient to let the bike carry the load, and then I power the bike.

I have an assortment of panniers and bags, but the current favorite is the Ortlieb Downtown commuter pannier:



It is a good all-around size for carrying a change of clothes and shoes and lunch. The QL2 system mounts the bag securely but allows it to be removed or mounted quickly, and it fits a range of rack tube diameters (I have a nonstandard rack). The top of the bag folds over securely (contents have stayed dry in extended downpours). It is VERY well constructed and durable.