Which streaming music service is the best?

My recommendations are Spotify and Google Play Music.

Spotify is the service I currently subscribe to, mostly just because I've had it for a long time now and as such, have a number of playlists. Unfortunately they don't support exporting playlists elsewhere. Spotify is also integrated with the PS4 now, so I use that a lot. What's also nifty about Spotify is that you can control it from any device where you're logged in, so I can have music playing via my PS4 and pick my next track or browse via my phone. I can't speak for its 40's / 50's selection, but you don't need a subscription for Spotify. You can check it out for free if you don't mind an occasional ad.

Google Play Music is the service I would be subscribed to if it wasn't for Spotify. Best features include being able to upload your entire music library so you can access it from any device just by signing into your Google account, complimenting the large streaming library. My favorite feature though is YouTube Music Key which is included with Play Music. This allows you to save YouTube videos for offline music, but more importantly, allows YouTube to continue playing while the screen is locked or you are in another app. I listen to a lot of remixes and live performances, so I have to set my phone to never lock when it's charging so I can listen to YouTube videos while I work.

My son got me started on Spotify. It works like Pandora, but allows you to save music for playing off line.

The ability to have off line play sounds good.

I like to listen to older music -- 1940's and 1950's. Does Spotify have a comprehensive catalog?

I haven't looked for music that old. All I can say is current, back to 70's is very good. Haven't had a problem locating a song yet.
It is free to try, so no loss of you don't care for it.

Thanks, I will look into it. I am also exploring iHeart Radio because it syncs with my Amazon Echo.