Small reality check
Wow, where to start....
First of all congratulations on stepping into this pretty far. Now for a bit of reality.
First, if you can't close it off, it's not technically a dedicted room. The doorways will have a large effect on not only the sound but where you can put seats, etc. If at all possible, serioulsy consider putting in double doors on those openings. To me, this is the single biggest thing that will help this space's potential. You can spend all you want on the rest but these holes WILL cause issues.
Second, wood floors are not necessarily a bad thing. Many recording studios use hardwood floors. The compromise is that if you have hard floors, you should have a soft ceiling. This can acutally be BETTER than a carpeted floor since it does NOT have to be anything you need to walk on!
Third, No matter which end you put the screen/speakers on, you're going to have placement issues with your main speakers. You'll either have them jammed right against a back wall (not good for imaging nor for bass response) or you'll have them so that one side will have its first reflection point in that giant hole of a doorway - but only on one side. This will cause a lot of imaging issues.
Lastly, I personally prefer fiberglass. To me you get a LOT more benefit from less thickness. Also, if you're going to cover it anyway then foam has lost its last advantage IMO (though I personally don't care for it's look anyway in most cases). Making absorbtive covered fiberglass panels is really VERY easy to do. The trick is finding someone who will sell you OC703 or something similar and at a reasonable price. Ethan Winter has some very basic drawings on how to construct panels on his Realtraps site.
Once you figure out what you're doing with the doorways, where your equipment will be, what your equipment will be, where your seating will be, what you're doing with the floor - then I can give you a better idea of specifically what goes where in the room.
For starters, plan on absorbing basically the whole front wall and hitting the first reflection points on the side walls (assuming one of these is NOT right in the middle of an open doorway which I'll guarantee you it WILL be for at least one panel for at least 1-2 seats)
Welcome to the madness!
Lead Acoustical Designer
I am serious and don't call me Shirley.