I would like to be able to identify the plants that grow "naturally" in the
yard. I would also like to just be able to identify plants in general.

You need a field guide to wild flowers. Go to the library & take out one or two
until you decide which one you want to buy. I prefer Simon & Schuster. I think
you want the Eastern edition, but I suggest you check. For trees you want a
field guide to trees & shrubs.

Botany nowadays, especially taxonomy, is changing almost as rapidly as computer
science. Your old books will not be useful, except as antiques. Go to the
botany library at the University of Michigan and tell the librarian what you
are looking for.

Would the Latin plant names in my "Plants of Michigan" from 1939 still be
valid?

A few might.
You also need to become adept at Web searches.


Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)