I am on paper patrol.
Last year I made a gazillion xeroxes and didn't know where they were half the time. The students never knew where their xeroxes were either. (To avoid losing them, I would copy them at the last minute, which is a dangerous game.) Afterward, I got the same gazillion xeroxes back for grading. I often returned them to the students late because I could never find them.
I did file important papers from the administration neatly and carefully--and never looked at them again.
I am making a Binder (capitalization intentional). Important things go in the binder or on the calendar. Everything else gets recycled. My daily schedule is first, followed by the plan for the week at the front. I call my plan for the week "The Halpern Pages." My daily plan says, "Check the Halpern Pages! Update the Halpern Pages!" I have the Torah Reading Page, the Tanach Page, and the Israeli Dance Page. Each will have the essential info for the week so I don't have to carry it all in my head. (I was doing this last year in a lesson plan book the school gave me, and it worked okay, but I couldn't slide papers in and out of it like I can a binder.)
For paper patrol on the part of the students, I took the advice of a colleague and did away with loose handouts. I am making each unit in advance (I've almost finished the first one) and will bind it or put it in a duo-tang folder for each student. That way, the student has his/her own "workbook." When they have homework I just check that they wrote something, but I don't collect and grade the folders until the end of the unit. The students will know exactly what the quiz is on because it's all in the folder, or workbook, or whatever. They can turn in the folders on the day of the quiz so they still have them to study with.
Another thing that will help with paper patrol is that I'm going to be in the same room every day. I have to share the room (obviously), but I will have everything I need right there instead of having to schlep stuff. That way, when I clear off my desk, I can grade papers* and put them in my "outbox" or wherever for the students to pick up, instead of putting them in a file folder of "papers to return" and losing it in a sea of identical tan folders.
*I assume I won't be able to do away with papers entirely. I'll have to grade bellwork several days a week as well as quizzes, not to mention extra stuff like "take the last 2 minutes until the bell rings to write down 2 things you learned today."