I would like to focus on modern Neapolitan music and in particular Luigi Libra.
There is the Canzone Napoletana, songs like ‘O Sole Mio, Funiculì funiculà, ‘O surdato ‘nnammurato, Torna a Surriento (Music of Naples - Wikipedia). When I was growing up, I came to know this music through Luciano Pavarotti. I recall my father would play the album Pavarotti & Friends on a CD player.
There is modern Neapolitan music, such as pop music. I enjoy listening to this music for light listening. However, the beautiful Neapolitan music (at least in my eyes and to my ears) is from Luigi Libra. In 2014, he was named the world ambassador for la canzone napoletana (Luigi Libra - Wikipedia). What I love about his album is that he has recorded modern covers of classic Neapolitan songs like Tu vuò fa l'americano.
He also gives Neapolitan music a modern interpretation by incorporating other instruments not used in Neapolitan music such as the jazz piano and taking out standard instruments such as the mandolin (Canzone napoletana - Wikipedia ).
Technically, Neapolitan music is not pure Italian (See the upper-right corner of the language tree below). However, Nap-Cal which stands for Napoletano-Calabrese is right beside Italian and belongs to the Italo-Dalmation family of languages. To me, the sounds of Neapolitan are heavily based in Italian (or vice versa) and the Neapolitan language provides melodious music that Italian learners could benefit from.
Here is one of my favourite songs from Luigi Libra
Nun è peccato di Peppino di Capri
I have not looked into studying other dialects. There are many in Italy. It is good to know that Italy does not have a uniform culture. Regionalism is quite strong and locals are proud of their church bell, il campanilismo (Campanilismo - Wikipedia).
The reasons that Neapolitan is nearer to me are the overlap with music (the Pavarotti from my childhood) and my Verbling Italian teacher was from the south of Italy. Neapolitan was one of his languages. I recall a discussion where he did not like how Neapolitan was spoken in his area rather than Italian. The irony of it is that he was not enamoured by his mother tongue, the beautiful language of Neapolitan but I, a foreigner thousands of miles away, could melt listening to Luigi Libra’s voice, which to me was like the Mediterranean sun.