A full-duplex scanner is worth the investment. I've configured mine so that it automatically drops the file on a network share for storage.

Receipts I ignore (the credit card transaction is caught by my online budgeting service). Random bills / statements get uploaded to Google Drive. There's a "silent OCR" that runs on the PDFs... you can't access the text directly or by API, but if you search for anything it will appear with high accuracy.

I've quit trying to organize anything since everything is easily findable.