Weird that we all get into this after a death in the family. My dad passed away a few years ago and first I wanted to digitize some old pics of him, but then it evolved into digitizing EVERYTHING from out family and my grandparents too. It's actually really fun going though all those old pics, which helps because its a massive undertaking. It becomes a little side hobby in itself.
So if you're willing to put in the time, getting a good flatbed scanner and cranking through pics is a good way to spend an evening while watch movies or something in the background. If you're less inclined to take up your free time doing it you may want to go towards paying for a service to do it for you.
Flatbed scanners are the most versatile and can give you great results but they're all slow, the Epson Perfection scanners are pretty much the most common scanners to get. If you have a bunch of negatives and already have a good digital camera, a camera based negative scanner works great and is pretty fast.
Scanning from negatives is always preferred if you can get them. Also think carefully of your organization and archiving. You're probably going to want to sort and organize them, and your organization may change later in your process. In my setup my computer folder structure matches my physical folder structure, each roll has the same folder name in real life and in the computer. Then with Lightroom I can use face tagging to identify people, Keywording to identify places, and add EXIF data to give approx dates.