For so long I gathered my scenario cards into a small number of ASL shallow boxes (Paratrooper, Partisan, etc) with a a box each for core, HASL, AP, General and Annual scenarios, followed by quite a few years when I did nothing with Journals. By about 2009 I started to scan any new stuff and gradually worked my way through my back log.
I use my scans when selecting scenarios. The core, AP and HASL ones went into the existing box collections for safe storage., the non-CH TPP stuff have their own boxes, the SP (SP & RP) still in their original plastic envelopes in own box. I did print off a small number of scans on light card, ASL 122, the VoTG and FB ones that came in Journals have been added in with the associated core and HASL collections as they have the same sequence numbers, but they were the only ones. MMP's Journal and HoB's RbF scenarios remain in their original magazines.
The paper and card originals are kept safely and will be rarely handled, working with scans on my laptop I find is far faster in finding what I want. I have arranged the files by a directory tree eg FB 12 is in "C:\Users\Paul M. Weir\Pictures\My ASL\Scenarios\Multi Man Publishing\Historical\Festung Budapest" in files named "MMP FB 12 a.jpg" and "MMP FB 12 b.jpg" for the 2 sides and both with Title of "The Black Ravens Are Flying" and Date Taken of "05/02/1945 01:00:00" (Title and Date Taken are metadata fields that Windows recognises). While HASL have their own directory, contiguous series like Annuals, Journals, APs, WOs, core (MMP) or similar (LFT, BFP, SP, RP) each are in their own single directories. I keep mine as ".jpg" files as Title and Date Taken are supported by Windows for these files while not (under Vista or earlier at least) for ".pdf". "jpg" files are fairly universal anyway.
When I finish my backlog (1985 pages done, 224 to do) I intend setting up a theatre directory tree where I will place shortcuts to the original image files. So at the moment I can select by producer, producer code, title, action date (or range). I will be able to select by theatre in the future.
I don't bother printing out when I have selected a scenario, I just read from the screen. So at the cost of a little staring at the screen and zooming in, there is no paper to print, worry about or get damaged. I have so many that they outweigh and out bulk my laptop. A lot of work scanning and adding the attributes but I feel well worth the effort, even for a solo dilettante ASLer like me.