Nice to see a new face in the world of progressive rock. I can't add too much to what the others said, but here's my advice:
You say you already like Genesis. Not too many people I know click with it right away, which tells me you are easily influenced by prog rock, a wonderful gift in this unique genre. You will find many bands with different tastes and styles, and soon one to call your own. I found Kansas very easy to like, as their songs are somewhat short (compared to, let's say CTTE or Heart of the Sunrise) and yet, somewhat "epic" as you put it. Magnum Opus, The Wall, Monolith are all good to try.
But it seems to me, your the Yes type of guy. Yes, is my absolute favorite band of all time. I love them like a son. Seriously. Jon Anderson's voice will sooth you, Wakeman's keyboards will astound you... (see Roundabout) You will see, you will see. And they have such a wide range of sound, there simply can't be one song you don't like. I would suggest Fragile, and pay close attention to South Side of the Sky, The Fish, Roundabout, and Long Distance Runaround. But if you want to hear all the bands greats, buy the 35 anniversary addition. It includes some of my favorites, Siberian Khatru, CCTE, HOFT, Tempus F., and tons more. Check out one of their newer albums, Magnification. I hope you can put things in perspective...
Now, some Genesis albums you can't miss: Invisible Touch, The lamb lies down on Broadway, and Wind and Wuthering. Can't miss.
Did anyone suggest Grateful Dead to you? They are superb. I highly reccommend Terrapin Station. It's long (about 16 minutes) and it has a new feel every few minutes. The album carries the same name. Also inside, see Passenger, Estimated Prophet, Sunrise... God, everything is gold. Just do me a favor, and don't listen to Workingman's Dead, or Anthem of the Sun
. I can't stand that!