For modern prog suggestions, I'd offer up things like latter-day Porcupine Tree (with Gavin Harrison on drums) or the two more recent Steven Wilson solo albums. I'd also like to throw in Flying Colors, which features Mike Portnoy of Dream Theater, as well as some very melodic songs with proggy-tendencies, which range from hard and heavy to some tender melodic ballad-type stuff. It's very pop-prog, but that might be a good introduction to some of prog's best players.
I'm sure plenty of prog fans on here will suggest their favorite bands, myself included, so it might take you awhile to figure out what suits your moods and tastes, especially if you follow everyone's blind suggestions. When I first started out, i fell in love with Rush, and from there, it just sort of expanded to Dream Theater, anything with Mike Portnoy, then anything with Neal Morse, then any of the major 70's prog acts (King Crimson, Yes, Genesis, ELP, Pink Floyd), to the "Third Wave" 90's prog bands like The Flower Kings and Porcupine Tree, all the way up to today. It's been a near 15-year journey for me, but I've discovered a LOT of different styles and subgenres of prog rock, and as much as I like, there are thousands more that I haven't heard, nor will I ever hear them.
Either way, best of luck on your maiden voyage into the progressive oceans!
-Marc.