One thing I find helpful for convalescent & nursing homes -- especially those with mixed-age residents -- is to look for songs that have had multiple renaissances in pop culture. E.g., Blue Moon, written in the 1920's, has reappeared on the charts in several decades; Bill Bailey, written in 1902, is a standard for jazz, dixieland, swing, and other kinds of bands; Danny Boy (much to the chagrin of Irish bands) is beloved by many generations; Any Time, Who's Sorry Now?, Ain't Misbehavin', and Stardust are others that have had several rebirths.
For instrumentals, I don't think it matters much what kind of music it is, as long as it is something you play well and enjoy playing. People respond to the rhythm, the spirit of the music, etc. For sing-alongs, obviously, there is a benefit in doing simple songs that can be learned easily and/or familiar songs that will stimulate all sorts of memories (beneficial for the sake of the memories per se and for the emotional or cognitive stimulation per se). Also, parodies of old familiar songs (e.g., "Let Me Call You Sweetheart, I'm In Love With Your Automobile") offer both cognitive stimulation and humor as a release.
One thing that never ceases to delight me is meeting, in retirement and nursing homes, musicians such as Benny Davis's sister (who was herself a jazz singer) and folks who played and/or sang with Kay Kyser, Tommy Dorsey, Duke Ellington, and the like, as well as former opera singers who can still sing circles around me in their nineties! I learn something from these folks just about every day.