I suppose it depends on what country you live in, but playing classical music in the UK is the same as any other kind of music - if you're playing it to the public, even a radio station, you need a licence from the Performing Rights Society. There's no problem at all in playing music privately.
As renegade600 says, the best way to play any classical piece covered by more than one track is to set up a playlist - or two if you want to listen to a Mahler symphony. You can also ask Alexa to play a whole album from your library. She has trouble with some composers' names; I had to remove "Suk" from my playlists and just use the name of the pieces.