I knew about The Cowboy Junkies mostly from The Trinity Session, their second album when first it came out in 1988. It was an underground sleeper for bit, and then it took off. I had heard of them (but not heard them) before because of their first album, which was only a minor local thing, mostly covers.
The Trinity Session was done in a style that was very old school back to the days of the first electric recordings (other than that it was done with DAT recorder). It was recorded all in one night in 1987, in a church with great acoustics, and with only one microphone. It is the album that Sweet Jane is from, but as most reviewers agree, that tune is far from the best track on the album.
There is a fair amount of live video footage of them on Youtube - Austin City Limits, Jools Holland, Massey Hall, etc. And there is a live recording of them together with John Prine, which I might've posted except that the cutesy graphics added to the clip are immediately nausea-inducing and I wouldn't want to be held accountable for the cleanup of your keyboards and screens. There was also once a very sultry clip of Margot Timmins and Jeff Healey (on acoustic guitar), just the two of them, floating about for a bit, but I can't find it now.