Hi WyoWmn.
Hmmm....a few that come to mind are:
''Hit The Road Jack'' (recorded by many including Ray Charles.) A minor, G major, F major, and E7th (or any other key you like.)
''Feeling Alright'' (Joe Cocker/Leon Russell version) (C7th - F 7th) (2 chord wonder!)
...some of the early Eagles tunes are pretty basic as well and easy to strum and sing to. (ie: Take It Easy, Best of My Love..etc.)