The batch process is for batching the work in PSP. You would have to identify what tasks you need to batch. I don’t think printing is part of the tasks that you can batch (although i am not 100% certain). Same with the scanning itself. But would you have to do some editing on those items? if they are documents, would they need sharpening? better contrast? Unfortunately, it COULD also be a one-by-one process if editing varies from item to item too.
For the scanning, make sure you scan at least at 300 ppi resolution if they need to be printed back (higher if you can).
As for the printing, maybe you can outsource that? send the images to a printshop?