For the BEST print quality, how should I save this banner in Photoshop CS3?

I would choose TIFF or PDF. If you choose Photoshop PDF: in Save Adobe PDF window uncheck Preserve Photoshop Editing Capabilities and Optimize for Fast Web Preview. In Adobe PDF Preset choose Press Quality (if you're going to use an external press service) or High Quality Print. Next click on Compression (on the left) and in Compression box choose None or Zip, then you can save.