For me, I wouldn't use a ballad simply because, while within their wheelhouse, it is not what they are known for, or what they are best at. I would want to introduce someone to Dream Theater, so I would use a song more indicative of what DT is, which the ballads don't really do, and could even set up a false sense of what kind of music DT actually makes.
Then you're not introducing anyone to DT. You are introducing them to your remix of DT.
Yeah, I mean if I was going to use a ballad, or one of their more pop-oriented songs, I'd tell them right away that this isn't what most of their music sounds like. I still think it's better if someone likes some DT than none though, but that's just me.
As far as the song edits, is deleting some jungle sounds out of IT, or shortening the ending of Misunderstood really a remix? Those are certainly not things DT is known for either. Wasn't that part of the reason the Greatest Hit compilation was created? Many of the songs on there have been shortened (some too much IMO, but still). I've shortened several songs for my own listening just because I skip certain parts anyway, and again those sections are ones a new listener could easily be turned off by, so I see no problem. But we may just look at it differently!