Speaking of taking a picture, apps like Scanner Pro, TurboScan, or Evernote Scannable do a pretty good job of scanning in documens using the iPad's camera.
As long as you have an iPad 3 or newer, and don't need a pixle perfect scan; these are good options. Cheaper and easier than trying to get a printer/scanner to work directly with the iPad.
Unlike just taking a photo, these apps will process the image for readabilty, crop it, and undo any distortion cause by not having the camera possitioned perfectly. (make the paper retangular again)
The evernote app is the least tweakable, but it's free. The others are priced reasonably if you think you'll use them a lot.
I mostly use Evernote Scanable to get notes, receipts, and other bits of printed information into my iPad. I only resort to Scanner Pro when I want the best quality scannded document I can get (short of using a real scanner).
This solution has worked so well for me that last time I bought a printer I didn't bother with an all-in-one. All I need from a printer now is that it print; prefereably using AirPring so I don't have to wory whether I left the desktop running or not.
Caveate: If I have my iPhone handy I'll use it instead of the iPad. It's not so much that the camera is better (which it is), but more about how awkward it is to possition my iPad, especially when it's in a bulky case.
Also, I haven't needed a high quality scan for a long time. I'm just recording stuff, and possible sending info to other's; not desktop publishing. It just needs to be clean and readable.