I think this may become a bit more of an "my experience with prog" than an educational thing. Though...I will try my best to make it both. So far i've done some of the educational stuff. But now, I think i'm going to go ahead and share my experience with said genre. I will start off with the first band that I got into in this genre, and will share a little more experience, I want to mix it up a little bit, so I won't share everything in this one post.
First bands:
The very first band that I got into in the prog genre was if I remember correctly, Dream Theater. I had listened to the Systematic Chaos album more than anything on my iTunes at the time. I was deeply impressed by the quick quitar riffs and even more impressed at how they were able to throw in the keyboards as an instrument on a studio album. Keep in mind that this was probably the first time I had ever heard the keyboards in an actual band. I soon started to download and purchase more and more of their albums, even today I probably have every one of their albums including EP's and stuff that was never released. They had easily made it to be my favorite band at the time. People thought I was weird because they tried to listen to them and instantly said they didn't sound good. I think it really depends on your taste if anything. Prog isn't a difficult genre to get into if you really dig the kind of thing that prog has to offer.
Discovering more prog bands:
Through time, I had started to realize that Dream Theater was not the BEST of the best, but they were certainly extremely talented in what they did. I also began to do some google searches and youtube searches on other prog bands that I would be interested in. That in itself had introduced me to the magic of "Progressive Metal". As I listed above, Youtube had actually introduced me to Myrath, which is now one of my all time favorite bands, all genres included. They have the sound that I look for in a prog band. The vocals are perfect, the guitar solos are unbelievable, and the rhythm is amazing. The day I had heard them was the day that I started really researching more and more bands in both the progressive rock and progressive metal side of music.