I plan to switch to a variation on this, based upon what I found in a big box of stuff from an old piano teacher -- photocopy sheet music onto one side of 8.5 x 11 cardstock, so you can lay them in a row with all pages of the song visible at once with no page turning.
Use archival quality book tape to tape the individual pages together, making "hinges".
Then you can fold the whole thing up accordian-style, and archive the sheet music originals someplace safe, like a filing cabinet.
This covers two concerns of mine, wearing out old sheet music (I have some that is over 100 years old), and having to stop and turn pages. As for where I store it, I outgrew the piano bench storage long ago. I use an old steamer trunk as a coffee table, and store the extra music in there.
- Spread loose sheets out on table in front of you
- Use adhesive tape to tape the sheets together
- Fold them up like a book
- Put three pieces of tape around the 'cover'
From here you can file them alphabetically or just leave them around - much easier to look for packages than for single sheets lying around everywhere!