Let me make this easier:
ORIGINAL LINEUP ALBUMS (the lineup that actually wrote and recorded its own music)
Live in Tokyo (found on the remastered version of the EP)
Rage for Order
Building Empires - DVD of live footage/videos, history of the band, good stuff.
Operation: LIVEcrime - historic live DVD/CD set.
Promised Land CD-Rom - old school CD-Rom video game released in 1996
Hear in the Now Frontier
Greatest Hits (various singles and a couple of b-sides from 1983-1997)
Tribe (minus the song "Losing Myself" which was a last-minute addition once DeGarmo left the band again)
Kelly Gray Era (DeGarmo's replacement, both as guitarist and major songwriter)
Live Evolution - nice 1 DVD and 2 CD set...Kelly Gray is a bit tough, given his different way of playing CHris DeGarmo's parts, but still a quality DVD and live release overall.
Tateryche (Queensryche spearheaded by Geoff Tate, who uses producers/outside writers to write the music and then has the band record it)
Art of Live - horrible live album. Don't buy it, ever.
Operation: Mindcrime II
Mindcrime at the Moore - double DVD/CD set of both Mindcrime albums performed live, more in a Broadway style production
Take Cover - covers album...horrible vocals
As bosk1 has stated, if you pick up Mindcrime II, just from a musical standpoint, it's decent through "Murderer." No sense in listening after that. Complete trainwreck. "Fear City Slide" is pretty good as well, probably the only track worth a damn from the second half of that record.
American Soldier is pretty decent, but like Mindcrime II, it falls apart. In this case, it falls apart after the song "Man Down."
The thing you have to remember about Queensryche is, anything that is not the original lineup, tends to sound very different. The songwriting style found in QR's original lineup records really follows a path of musical evolution. The non-original lineup stuff sticks out a bit like a sore thumb, since a different person is writing the music...
Not because it is all BAD, but because the primary songwriter is different. In the original lineup, it was Chris DeGarmo and Michael Wilton writing most of the music, with Tate and DeGarmo doing lyrics and melodies.
In the non-original lineup stuff, Tate does ALL the lyrics and melodies, and the music is written by whatever writer is working with Tate. So it doesn't sound like a natural progression at all. Not always terrible, some stuff is very good, but it doesn't really sound like the same band, musically, for the most part.
After the original lineup, I'd recommend these SONGS:
Right Side of My Mind
When the Rain Comes...
Operation: Mindcrime II
Hostage (this track actually was supposed to be for Tribe, and is the only song on Mindcrime II that does not have Jason Slater co-writing it -- the difference between the Tribe demo and this finished product is that court room drama sound effects were added, and Michael Wilton's original, fast-paced, ripping solo was replaced by this harmonized mid-tempo one, recorded by Mike Stone, which isn't nearly as good).
Fear City Slide
One Foot in Hell
At 30,000 Ft.
A Dead Man's Words
>>>>>>>>But my overall Queensryche recommendation is to buy all the original lineup stuff first, and if you want to continue, sample the other stuff and buy accordingly. Like I said, there is some good music on the non-original lineup Queensryche records...but it IS different, since the songwriter is completely different.