This is a gross simplification, but I hope its a good starting point.
Lightroom and Aperture are designed to manage groups of photos, and help you keep them organized. They also do image editing - but their starting assumption is that you have bunch of photos that all need to be white balanced, tone corrected, etc.
They assume that you are going to use any single photo for a variety of uses. This means any image editing you do by default does not change the original image, the changes are recorded in a database. LR (and I believe Aperture) assume that you are going to "Export" the image you are working on so there really isn't a "save" option. You "Export" a copy of an image that you have edited for a particular use. Perhaps next week you have a new use for that same image, so you start from the original image and "Export" a different finished image for that different use (Print vs Web, for example).
Photoshop (and similar programs) start with the assumption that you are going to work on a single image and transform it into something better. If you want to keep the original image you need to archive it first and/or start with the "Save As" command. Photoshop assumes that you are generally working one image at a time (though of course there are ways to automate a task and apply it to multiples of images).
Photoshop has extraordinary controls to manipulate a single image. LR and Aperture do not come close to the power that PS has to transform a single image. Most people use no more than 5% of the power that PS has.
I would not start with LR or PS to begin with, they are both expensive and priced for professional work. Even if you decided that one day you would be at that level, you will probably find that by the time you got there you will have paid for several upgrades on versions that you weren't fully using. I believe Aperture is not as expensive, and so you might want to consider it if you think you have the need for a very robust digital asset system.
If you have an iMac, I suggest you start with iPhoto (Apple's consumer level image management program). It has been called "Aperture Light" by some (I have no direct experience with Aperture). With iPhoto you will learn about organizing digital assets, key wording, calibration of your monitor to your printer, doing tone corrections, white balance, etc etc in an affordable and easy to learn package. But not immediately - first you will have fun with albums, folders, printing calendars and Apple Books, etc etc And don't be fooled, iPhoto is also a powerful program. In time if you outgrow it you can upgrade to Aperture easily, or to Lightroom with only a little more effort.
I don't know and can't recommend what image editors (like Photoshop) you could start with, but there are several out there for Macs. I've always used the full Photoshop (since version 3!) and have no experience with the more entry level programs. I have Lightroom, and use it for the bulk of my digital image management, but I still keep iPhoto around because it does some things that Lightroom doesn't.
From reading the threads here, I suspect that your natural upgrade path from iPhoto will be to Aperture, in a few years time.
Good Luck. I know how you feel about leaving film behind, though I'm contemplating an Epson v700 scanner so I can go back to my medium format system. I have a good collection of glass for it.
), and, over the weeks and months, I proved to myself that you can teach an old dog new tricks.