Most of my comments have already been posted in the related threads linked to at the top and/or stated by others above.
I've been doing music full-time for the gamut of "senior facilities" for over 12 years and I manage to make a very very modest living at it, provided I put in the necessary "tedium hours" (on the phone and computer doing promo, booking, and record keeping).   As for repertoire, I find the larger and broader, the better. Some of my clients are Jewish homes, where having some songs in Yiddish, Hebrew, Ladino, Russian, etc., really helps, as does familiarity with musicals such as Fiddler On The Roof.   Some rehab and convalescent homes value my services because I can sing Ya, Vi Elsker Detter Landet for their Norwegian-American residents, De Colores for their Spanish-speaking residents, Sakura for the Japanese Americans, etc.   But knowing songs (especially soft rock and country) from the '70s and '80s also comes in handy for rehab centers and some group homes, where the ages may range from young adulthood (or occasionally younger) to over 100.   
I do get a lot of requests for "songs from the '20s, '30s, and '40s," but there are also specific frequently requested songs that go back as far as Stephen Foster or were popular in the '50s, '60s, '70s, and '80s.

Familiarity is valuable, partly because music (especially participatory music) can stimulate both memory and emotional release.   But I find some songs -- e.g., Ripple and a couple of my own compositions -- are very well received even by people who have never heard them before.

What I usually avoid are wordy songs that require uninterrupted attention from the audience.   Some independent-living settings work for that type of song, but nursing homes and even assisted living residents seldom do. Many residents tend to be easily distracted, plus in many settings the visitors and staff tend to think nothing of upstaging or interrupting the residents' activities.   (It's not unlike singing in a bar, in that respect.)

As for pay, well, I use a sliding scale.   Some places pay me two or three times what others do. That's partly because facilities' budgets vary widely and partly because, frankly, some gigs cost me a lot more in time and money "overhead" than others do.   I basically negotiate a fee with each client, and generally I am paid from about $30 to $70 for a one-hour program. Few of my clients (Portland, Seattle, San Diego areas) can/will pay more than $70 for a solo performer and I usually am unwilling to do a program for less than $30 (e.g., nearby gigs that take hardly any time for booking, billing, etc.) to $45 (less frequent gigs that cost me more in gas and time).   As I tell clients who ask me:
If I asked everyone for $60-$70, I'd work half as many jobs, because so many can't afford that.   If I charged everyone $30-$40, I wouldn't net enough to keep doing it.

(When I talked with a local musicians union a few years back, I was once told that I should charge no less than $60 for a gig, regardless of location or length of program, but that their rules did not mandate charging more for travel time/expense or for longer sets. In other words, I could drive 150 miles and play for 3 hours and the union would allow me to ask only $60, but if I played for my next-door neighbor's kid's party for 15 min., I should also charge $60. Maybe it's just me, but that seemed kind of silly.) ;D

By the way, as for "making money" from the use of copyright-protected songs at retirement homes, I have a feeling anyone trying to prohibit the use of golden oldies and standards in those settings would have about as much luck as Disney did when they tried to keep the Boy Scouts and Girl Scouts from using their songs at camp.    It would be pretty easy to demonstrate that, with the low pay most music therapists and entertainers are paid in retirement homes, all the expenses they incur in providing those services, and the inclusion of public-domain songs (e.g., songs written before 1900), the providers are actually losing money from such use.