I asked my son who is an accountant about this, and it seems like tons of computer programs provide the features you're looking for. Look for something like Microsoft Sharepoint (that's the most popular program but my son says there are hundreds of cheaper alternatives that are almost as useful). The option to set a destination folder for every new scan is called automated routing, and it works by way of optical character recognition (the ability of a program to "spot" a phrase or a word in the latest scanned document and "understand" it). In practice, it means that once you scan something, the program will decipher what that document contains and find the appropriate folder to store it right away. It "reads" the scan and will group it with similar ones. Here's a guide about how you can quickly set that up when using Sharepoint, it should be similar to every other program of that type (have your 15-year-old relative take a look as well, though I think it's not that hard to follow).
But what about photos that don't have writing on them? Well, for those you can simply set a rule that every upcoming scan will end up in a specific folder of your choosing. That means it'll be best to put the photos aside in one pile and when you scan them ("digitize" them), set a rule that all upcoming scans go to the "pictures" folder, for example. Of course, you should double-check if all goes as planned at first, and make sure you can find that folder easily after you're done.
They're actually using two such programs at my son's office since some features cost extra and they have only a monthly subscription for one of the programs, while they've bought the other one. They're also following retention schedules (something this article covers) about hard copy file management to prevent them from blocking their workspace with outdated documents. Obviously, with the number of invoices and business plans they prepare on a daily basis, they have to do clean-ups like you're about to do with the storage room at least once a month.
But, for your case, he says it'll be wiser to simply pick a program (these are called document management software or DMS), and sign up for a free trial. Cleaning up that storage room shouldn't take you more than one weekend, meaning spending money on that will probably be a waste for you. Hope this helps and I'll say "thank you" to my son in your name
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