No clear idea of scope yet
I think you are seeking an above average system. I do not have a clear idea of the scope of it. Are you intending to completely rebuild the room or not? If you are 15K is not realistic.
If you are intending to just wire the existing room and furnish it that is a different matter.
I think you are leaning towards a projection system. Not a bad idea if it is a windowless basement room.
I would start by picking out your speakers and video system.
In your price range, I recommend people audition speakers from manufacturers that can build products for the professional monitor market. Usually, but not always, their expertise filters down to their more cost effective offerings.
I would make a strong recommendation for you to audition the B & W 684 theater system.
http://www.bowers-wilkins.com/display.aspx?infid=2354&sc=ht
For a projection system, I think Epson have a reputation for providing good value for money.
http://www.epson.com/cgi-bin/Store/ProductCategory.jsp?BV_UseBVCookie=yes&oid=-13921&ref=r0302EDb3R&s_kwcid=epson%20projectors|630523020&gclid=CN_82uaB6o8CFSIZWQodZQ2DEQ
I would certainly consider an acoustically transparent screen, then you can mount the center channel behind the screen. ClearPix2 are THX certified.
You can then choose a receiver from a well known manufacturer. I would aim for one than can deliver about 100 watts per channel. Select the one that has the facilities you want. For instance does it have enough HDMI inputs for all the peripherals you intend to purchase. Talking of HDMI inputs make sure they have true repeater architecture, otherwise newer equipment might not make a handshake with it especially cable boxes and HD DVRs. Also it is probably worth seeking out a receiver that has the latest HDMI 1.3 standard. That supports the new lossless Dolby and DTS codecs that have been developed for the new HD discs. Also if you are going to get an HD disc player, make sure your receiver can decode these new codecs, and you won't have to use Dolby 5.1 with the AC3 lossy codec.
If you are going to go the HD route, I think the HD DVD/Blue Ray battle will likely be decided this holiday season. The way I read the tea leaves, I think HD DVD is getting ready to run all over Blue Ray, but obviously I can't be certain. At the moment I'm still sitting this one out. However I think the recurring theme of "wrong pony Sony" will play out again.
I would recommend that you get an HD DVR that is compatible with your cable or satellite service.
Lighting is important, here professionals can guide you. Furniture needs to be smart and comfortable. I had sticker shock with that one.
One other thing, if you are going to take the walls down, and if funds permit that would be best. Then the walls can be replaced to proper specs. If the walls do come down, I would strongly recommend going to the trouble of putting in conduit for the cables. Then when technology changes, it is a very simple matter, and cheap, to change them.
Look at these pictures of my construct and you will see what I mean.
http://mdcarter.smugmug.com/gallery/2424651#127095358
Finished product with all cables hidden.
http://mdcarter.smugmug.com/gallery/2424008#127077317
I'm atypical, as a I roll my own speakers, I always have. I build some of the other gear as well.
There is a lot to think about and consider. Don't rush. Evaluate your options carefully. Properly done you, your family and invited guests will have some great evenings. Good luck, and keep us posted on your progress.