Dream Theater Greatest Hit (and 21 other cool songs) is 2 hours 18 minutes long. That's long enough for 40% of the entire MM era... and if you discount The Astonishing (because of it's abnormal length and odd format, not because of the music) you could fit literally about 70% of A Dramatic Turn Of Events, Dream Theater self titled and Distance Over Time on a double album that long. And even though The Astonishing is long, it has a lot of repeating themes and redundancies, so it'd be quite easy to pick a strong sample of a few songs from it. So I guess what I'm getting at is that it'd be pretty easy to make a greatest hits for the Mangini era without having to make many hard choices if I'm allowed an album as long as DT's first Greatest Hits album. For that reason I think it's only an interesting question if it's restricted quite a bit to be under 90 minutes at the most
Breaking All Illusions is probably the only must for me on the album as well. But I agree with what's been said that On The Backs Of Angels belongs on the album, and it's a strong song anyway. And if I'm trying to build something that actually could be a Greatest Hits I probably wouldn't just pick my favourite songs in order until I hit the time limit.
So, my semi-realistic MM era Greatest Hits single disc:
1. On The Backs Of Angels
2. Fall Into The Light
3. The Bigger Picture
4. At Wit's End
Mini-Astonishing Suite:
5. The Gift Of Music
6. Three Days
7. A New Beginning
8. The Enemy Inside
9. Bridges In The Sky
10. Breaking All Illusions
Length: 78 minutes
Turns out this includes the lead single from ADTOE, DT12 and The Astonishing, and the second single from D/T (Untethered Angel would be too similar to OTBOA and The Enemiy Inside, and Fall Into The Light is a much stronger song). It hurts to leave Illumination Theory off, but for DT12 material you could get The Bigger Picture, The Enemy Inside and Behind The Veil for less track time than Illumination Theory, and realisticically that is probably better for a greatest hits album. The Enemy Inside and Behind The Veil are actually my preferred tracks, but I think that The Bigger Picture gives more variety and a better representative of the DT12 material if you can't have Illumination Theory, and Behind The Veil is a bit more similar to it than The Enemy Inside (plus The Enemy Inside is a lead single and gives us a relatively lean fast paced heavier song).
The Astonishing picks are among the strongest tracks on that album imo, but they also give you at least some taste of the story, and arguably they tell the central story in about as short a form possible - land without music, savior with his magical guitar, conflict with the oppressive ruler, resolution through shared love for someone and appreciation of music. Obviously a lot left out (unfortunately none of Arhys' conflict, you could highlight that part instead of Nafaryus and Faythe by going for Moment Of Betrayal and Path That Divides instead), but I feel like you could make a lot of sense of things and feel some jounrey of a story with just those tracks.
At Wit's End and Breaking All Illusions are some of the highlights of the MM era and provide our DT epics for the greatest hits, and Bridges In The Sky was my pick as I think it and Outcry are the next strongest songs and Bridges In The Sky just seemed a better fit here - it's tough not to choose two shorter length songs instead such as say S2N, Behind The Veil or Barstool Warrior. We're probably missing a proper ballad too but there's a lot of lighter stuff here already.