How big an air compressor

Note that you aren't directly concerned with tank size here, so much as the power requirements of the motor. It's perfectly possible for two compressors to have wildly different tank sizes and the same pump head and motor, and likewise for two to have the same tank sizes and quite different compressor heads. (It's also generally true that larger tanks and larger motors/pumps go together.)

Compressor horsepower measurements are...strange. That said, I think you're looking for something in the general range of 1 HP or so.