I have used two long plastic boxes to organize my gift wrap. In my past apartment, I kept both boxes under my bed in our master bedroom. I have one for general gift wrap for birthdays and showers. The other box has all Christmas wrap. I keep all of my ribbon and bows in a big bag right now.
The plastic boxes are great to see what type of wrapping paper and bags I have inside before even opening the box. I would suggest getting these boxes. They are on Amazon and are so easy to stack and store anywhere!