Another tool in your arsenal against paper will be scanning. You only need the original, paper version of very few things. Think:
Social Security Card
Other than those, I can think of very little for which a digital copy won’t suffice. In light of that, as you’re sorting your papers in the coming days, I want you to think about scanning as much as possible.
For basic scanning, the Scannable app by Evernote is easy to use and doesn’t require an additional device. It’s a phone app that allows you to scan and then upload directly to your Google Drive or other cloud environment. The quality isn’t as good as a stand alone scanner, but high DPI isn’t really needed until you start scanning photos that you may eventually want to print again.
Download Scannable or borrow a friend’s scanner for the duration of the month
Gather up the important documents listed above and put them together in a file, safe or envelope so that you know exactly where they are.