Many years ago I got a Corel Photoshop Pro package for free (after rebate) and learned to use it and liked it. After changing computers, I couldn't get it to load and wasn't going to pay for it, so...after the recommendations made here...I got PhotoScape and have been reasonably happy with it.
You've read right, if you feel like learning the whole thing. Our needs in coin imagery postprocessing are simpler. Cropping, sizing, sharpening, maybe some elementary hue correction for white balance, that's it. It can be learned independently of Gimp's vast capabilities - the same can be said of any graphics software. I know very little of Gimp's total capabilities, ten years in. I don't need to know it.
I had a really nice simple photoediting program that came with my first scanner but I couldn't find the disk when I switched computers. Then I had a copy of photoshop for awhile, but when I switched computers again the disk was corrupted and wouldn't load. Now I have Photoshop elements 8 which I am still learning. I tried to go with Gimp, but while I was able to download it it will not install. I haven't tried PhotoScape yet.
I use Lightroom and photoshop. You may have seen some of my photos if you drink corona or jack Daniels
Well, Gimp is free Open Source software. It'll never cost you a penny, which is its' attraction. A graphics software every bit as powerful as Photoshop, costing you nothing. It ought to be the first thing you download the moment you want to go beyond basic graphics processing. PhotoScape ought to be sufficient for that basic stuff (I don't use it so I don't know how good its' Sharpening routines are), and enough for a typical coin photographer, so you don't have to use something like Gimp. The key there is how you acquire an electronic version of them, not the software you then process them with. You're going to be presenting PhotoScape with a .jpg or a bitmap either way. You'll want a pretty high-quality scanner, and the technical aspect of digitizing slides is different than that for digitizing photographs. Some scanners are better at the one than the other, and some do not do well with slides at all.
I just got through scanning in 50+ old family photos using a Canon 2420 printer as a scanner and PhotoScape as the storage place. I scanned them and stored them as both jpeg (for printing or viewing) and tiff (for editing) files. I then burned DVD's for members of my family...worked pretty good.