Update:
I tackled Disintegration by The Cure a while back. I liked the first song a lot, and a few others were good, but as a whole, I got bored after a while. I might need something more accessible with them.
Can't remember if INXS was recommended by anyone in this thread, but I am digging into them a bit more now. Kick has been a longtime favorite of mine, and I've always known a few of their other hits, but not much else. Digging some of these songs I have never heard before.
Also, INB4 Joe tells me he saw INXS x-number of times back in the day...