Personally, when I want to delve into "new bands", I avoid live or compilation material.
But it can work for other folks.
I find that actually seeing them play the songs gets me way more involved and interested quickly... SEEING live stuff is great for me, but I wouldn't start off listening to live stuff.
For OP's request, if listening first is your first choice, I'd just say go with Distance Over Time, since that's what you like so far, and then I'd go Octavarium.
I'd save Images & Words and Scenes From A Memory for the next batch and then I'd venture into some live stuff and go with Breaking the Fourth Wall and SCORE before moving on to the rest of the albums.
The only comment I have is what NOT to do. Dream Theater albums need to be heard as an entire entity, so please don't get the Greatest Hit(s) record thinking you'll hear a good cross-section of their material.
Uh, no they don't need to be heard as an entire entity, and going for The Greatest Hit is a also a nice choice and you WILL hear a good cross-section of their material.
It's not the tape-age or the record-age any longer where you pretty much have no choice *but* to listen to something in order. Starting with CDs the "random" option became the status quo and it's now ubiquitous.
If people have the time to dedicate an hour to just sitting there listening then sure, go for it in order and in its entirety, but don't scare people or try and shame them into thinking a single track played out of order/context isn't cool, cuz it most certainly is cool and for many people who just don't have the time for music anymore it's essential to be able to grab a track and go with it.