Best method to get out to the masses? The internet. Youtube, soundcloud, bandcamp, spotify, these places can be accessed by almost anyone anywhere in the world. Throw your/their stuff on there and boom, the masses can listen to your work.
Is social media enough? Depends. Some artists can get by completely without using it, others could use it daily or even hourly and it won't affect their popularity in the slightest.
Online fan connection to build their career? I mean it couldn't hurt.
Best tool to market their music? Get hooked up with a really good PR firm. Find a really good label that deals with your style of music. Find DJs/youtubers/radio stations/instagram or snapchat or worldstar celebrities and have them play your/their stuff. Find whatever gig will let you perform and perform perform perform.
Final thought, if you/they really want a career in music, whether it's performing or composing or whatever, you/they really have to look at everything and everyone that's already out there, then look at themselves/their work/yourself/your work and ask "Is this marketable?"