I went with the proggy side. I came into Dream Theater from being a fan of Rush. Around 2003, after having gotten into Rush for about a year, I was thirsty for more music like them, and after doing some research, a lot of fellow Rush fans pointed me towards Dream Theater, particularly their earlier works like WDADU, IAW and SFAM, so I checked those out and was blown away (I try to get a band's debut when I start out, and then their most beloved albums next). I was by no means a metalhead, and Rush was about the hardest hard rock I'd listened to at the time.
It didn't take long for me to get as many DT albums as I could throughout 2004. I remember being on Christmas vacation in California, visiting family, and I bought my Live At Budokan (either just the DVD, or the CD as well, I can't remember), and I was captivated. Train Of Thought was their most recent album at the time, and my excitement for Octavarium was through the roof, and being a mostly proggy guy, that album was everything I wanted and more (especially the title track).
Dream Theater really opened me up to heavier prog and prog metal, in a way that Rush, Genesis, Yes, or King Crimson did not quite achieve, but without those guys, I probably would not have ventured into Dream Theater with as much excitement and enthusiasm. They are my second favorite band after Rush, and I wouldn't change that for the world, but by far, I am in there for the prog - the metal is just made more awesome with the prog, and I'm okay with that as I have grown to love all their sides.
-Marc.