The absolute best way to digitize them is with a dedicated film scanner, but you're looking at around 3 to 4 hundred dollars, if not more, for a decent one.
Flatbed scanners have adapters for slides and negatives, but they're not as sharp as with an actual film scanner.
Here's a comparison I made scanning a slide with my Epson flatbed scanner, and with an actual film scanner:
Full frame, flatbed:
Full frame, film scanner:
Cropped enlargement, flatbed:
Cropped enlargement, film scanner:
The difference isn't just resolution, or dots per inch. A flatbed scanner simply isn't capable of focusing properly on a transparency, as the slide or negative isn't actually on the glass surface, there's a slight gap.
It is very time consuming to scan the slides, especially if you need to make corrections after scanning for color balance or exposure, and you usually will. My own workflow is at least 5 minutes per slide, usually closer to 10 or 15, with some taking a couple of hours before I was happy with them!
The scanners, either flatbed or film, will come with software, but the best software that I have found is Vuescan. It supports about a billion scanners, the license is not expensive and is forever, with updates forever. If you're a Photoshop user, Vuescan becomes available in the Acquire menu in Photoshop. Finally, make sure your scanner supports an infrared feature called ICE, which is capable of filtering most dust out of the slides, saving you
years (figuratively speaking) of effort cleaning the digital images. It makes the expected passes for red, green, and blue, and then makes an infrared pass. Anything that shows as a shadow on the infrared pass is not part of the image, and the software subtracts that from the image.
A Kodachrome slide of my aunt from 1954, unfiltered, then filtered by the scanner. I did not do any of this manually by cloning or healing brush in Photoshop:
Finally, a comparison of duplicating through the camera vs. film scanner:
Full frame, DSLR dupe:
Film scanner:
Crop of the center, DSLR dupe:
Center crop, film scanner:
As for initially viewing the slides, I had the advantage of Dad's slides all being in projector trays already, and I had his projector as well. Without projections, a light table is about the best you can do, but you
will need magnification to really examine the images.