Musik » Best way to listen to an artist's work?

I've been wanting to get into musicians more, basically established artists i'm interested in but have only heard a few songs of, but they have a substantial back catalogue. What would be the best way for me to go through their history of work. Buy and listen to all their albums in order, or watch their music videos first? (for songs that had them so then i'm seeing them perform art alongside the song aswell as the pop culture that may be attached)
Then if i love certain songs, i can watch live performances of them afterwards.
I was never really into music in such a big way which is a bit of a shame, so would like to change that!

I didn't find the right solution from the Internet.

References:
https://forums.digitalspy.com/discussion...an-artists-work

Product Video Example