I've had a Fujitsu ScanSnap S1300 for ages, and have recently been making a bigger effort to keep on top of scanning & shredding. A couple of tweaks have helped a lot with this.
The first is installing the ScanSnap ix500 software over top of the S1300 software. This comes with a separate application (Scannable PDF converter) for OCR-ing the PDF files. You can choose this as the destination for the ScanSnap manager, and then also set ScanSnap manager to do its work in the background (Preferences, Status Display, uncheck "Show the scan progress status").
I then used the instructions on this page to make the Scannable PDF converter app run in the background. Note that I'd already set it to OCR the files immediately, and had set up the directory structure to scan into.
Now when I have a spare moment I just put a document in the scanner. Even if the computer's screen is locked, the scan and OCR take place in the background, and if I'm using the machine nothing shows up on screen.
All the resulting files end up in Documents/Inbox, and I've put a shortcut to the Inbox folder in my Finder sidebar. I've also configured the View settings for the Inbox folder to show just the name of the file and date added, with a large preview pane beside the folder list. I can then easily work my way through the scanned files.
Next I'm going to start using Hazel to pick out those files which are easy to move into my folder structure and automate their filing.