The two best Adobe solutions for this are Lightroom Classic (not the more basic Lightroom app) and Adobe Bridge.
Both Lightroom Classic and Bridge have extensive tools for image organizing and applying metadata (such as keywords and captions). Both can work with your existing folder organization, and both also provide “collections” (virtual lists) and “smart collections” (saved searches based on a wide range of criteria). Collections are extremely powerful because they are independent of folder structure, so the same set of images can be used for any number of collections (like a book, a slide show, a web gallery…) without consuming storage space with duplicate files, because they’re virtual lists that all refer to the actual files in folders. Both apps also let you filter the current folder/collection, so for example if you want to see all images in the current folder that have both “Mom” and “Dad” keywords, you can do that instantly.
Those are some of the biggest advantages to using “digital asset management” software: Being able to get beyond the limitations of a hierarchical file system (folder tree) and just file and folder names.
The main difference is that Bridge is a straight file browser like the Windows/Mac desktop, while Lightroom Classic requires “importing,” which really means adding file references to a catalog. (The original files remain out in the normal file system.) Another big difference is that Lightroom Classic is tightly focused on photographic images with some video support, while Bridge supports practically all file types created by Creative Cloud apps such as images, PDF files, InDesign layouts, Illustrator vector files, and video (Adobe Premiere and After Effects).
Personally, I strongly prefer Lightroom Classic because I think it’s a mature organizational system, its catalog lets it do a few things Bridge can’t do, and I’m comfortable managing the catalogs. It’s also my opinion that Lightroom Classic is a lot more productive, partly for having lots more keyboard shortcuts. But you should be aware that a lot of people greatly dislike having to manage Lightroom Classic catalogs and get along better with the direct folder browsing of Bridge. So you might have to try both.
I also like the ability to add labels, as this seems like I could label who's in a photo and then later search for the name and be able to pull up all the photos of that person.
By @ShawnB01
Be careful with the “label” terminology. Both Lightroom Classic and Bridge support color labels with associated text, but they don’t transfer well among apps because they’re not really standard. If you want durable, widely compatible organization based on keywords and captions, use the specific IPTC standard fields such as Keyword and Description/Caption offered by Lightroom Classic, Bridge, and many non-Adobe photo applications too. IPTC is so standard that many photo websites automatically recognize and display IPTC fields found embedded in images.
If you use the proper IPTC fields in Lightroom Classic, Bridge, Photoshop, or non-Adobe photo software, they’ll be recognized on just about any device today. Not many realize the OS-level desktop search feature in Windows, Android, and Apple macOS and iOS can see embedded metadata such as keywords, description, location, and more. This means family and friends can find images on their computer or phone based on people names in embedded keywords, even when none of that info is in the image filename, and even if they’re only using the OS search feature (that is, they haven’t opened any apps at all).
If you want to study more about effective photo organization, you might try one of the books by Peter Krogh such as “The DAM Book 3.0” (DAM = digital asset management). He’s helped major media companies organize very large numbers of images.