Renaissanceman,
Welcome to our world of craziness. I don't have as much experience with this stuff as a lot of others, but I was pretty much where you are about 10 years ago.
In looking at building a system, consider whether you want to focus on surround sound or music. I think your main focus is stereo rather than surround, but you say it's going to be an A/V room, so I'm not quite sure. This is what a great salesman told/asked me the first time I walked into a hifi shop looking for a system...
Are you sure you need surround sound? What do you watch. If you're like me and mainly watch sitcoms, comedies and March Madness, you might not miss surround sound as much as you think. A great 2 channel system (with or without a subwoofer) could sound a lot better than a surround system for equal money. Using round numbers, a $1k 2 channel integrated amp will sound better than a $1k AVR. 2 speakers for $1k will sound better than 5 or more speakers that total $1k. 2 speakers set up correctly can easily give you a front right, left, and center channel speaker effect. I know this first hand, as this is what I've been using.
But if you're into surround sound effects like bullets quizzing by your ears, 2 speakers aren't going to cut it. That's something you need to evaluate for yourself.
Some people will say to integrated a 2 channel system into your proposed surround system. This can be accomplished, but it's a bit of a hassle (using a 2 channel integrated amp and an AVR).
If going the 2 channel route, I'd recommend getting the best amplification you can afford. Some people recommend speakers first, some recommend source first. Neither of the 3 approaches are incorrect IMO. I recommend amplification first, as I feel that's the potentially longest term investment in a 2 channel system. Getting the most neutral amp that gets out of the way the most sonically will stay with you during upgrades/changes to everything else. Source formats come and go. IMO people change speakers for frequently than amplification.
A few years ago I bought a Bryston B60 integrated amp when I first started upgrading the system I bought in college. The B60 has stayed in my system through every change I've made. Every change I've made has had a definite sonic change, which tells me the B60 isn't holding the system back. Through owning it for the last few years, it's become quite apparent that it gets out of the way and let's the music flow. Not to mention that Bryston amplification has a 20 year transferrable warranty, and I think you can see why I'm recommending amplification first.
Don't skimp on the source! People have the mentality that digital is all 1s and 0s. It doesn't all sound the same to my ears. For a mix of movies and music, I'd recommend looking into a universal player, and getting an outboard DAC for CDs. That way you've got a great video player, and the music side is handled by a 2 channel hifi component. Or you could look into a streamer like a Sonos or Squeezebox and connect that to a DAC.
Speakers must be appropriate for the space they're in. Huge speakers in a small room can sound just as bad as small speakers in a huge room, albeit a different type of bad. Don't rule out monitors augmented by a sub or tower speakers. 19x13 doesn't sound like a room that's big or small, but the ceiling height, if it's open to other rooms (and if so how big is the opening and where) and what else is in the room will dictate which will probably work better.
The biggest thing in a system IMO is the room-speaker interface. How the speakers fit the room, where the speakers and listening chair are placed, and the room acoustics are far more important than the electronics IMO. I've heard great systems sound like crap in a bad/poorly set up room, and I've heard systems I thought would be mediocre at best sound fantastic in rooms that were optimized for the stereo.
Before getting into what gear to buy, I suggest getting a copy of Jim Smith's Get Better Sound book. It'll give you an idea of how things should be set up before you start bringing in stuff. You could even use some of his tips to maximize what you've currently got. It gets a bit obsessive compulsive, so don't get overwhelmed.
Lastly, I recommend finding a good dealer or several. Let them know your goals and that you're upgrading one piece at a time. Hear complete systems at your proposed budget, and above and below it. That way, you'll know what your budget will get you. Maybe spending a few dollars more will make a huge difference, or maybe you can get what you want for a bit less. Only one way to find out. Furthermore, if you hear complete systems, you'll know what the end result will sound like.
Seeking out local audiophiles and clubs is a great way to hear stuff too, so long as you're hearing stuff you can afford.
Just some thoughts. I didn't think the post would be this long.