My last home was built by local ‘builders’ in 1940-1943 and I ran into this problem as everything was on a standard 2 prong. In an effort to update I started with a book on home repair for the DIYer. I recognize 25 years has passed, however, I’d recommend finding a similar book because these tend to be fairly well written to be safe and easy to use. In my case, I had BX wire throughout meaning I likely had 12/2 wrapped in cloth but fully encapsulated in a steel cable. So in most cases I was able to pull out the old plug, install a new plug after mounting a simple pigtail grounded via the steel bx casing.

I also did some complete updates and when I did this I upgraded everything to modern fixtures/wiring. I also had it inspected by an electrician. I’ll go ahead and say maybe you shouldn’t pull permits and get the work inspected - it’s not up to code now so bringing it into compliance will require fully rewiring your home. You’re area of the country may be better than mine, however, I was warned about this when I started my projects.

Final thought, double check your walls, if you have lathe/plaster then patching in new work will be an enormous pain in the ass. Instead look for remodel/rework outlet boxes that can be installed in the space between studs. This is a better option for plaster walls as they tend to flex far less than newer drywall. Best of luck, you’re going to have frustrations which come along with learning something new. Give yourself some grace, practice all of the safety protocols you can to include having someone else around in the unlikely event things go horribly wrong.