You might also want to consider getting the Apple 30" display, a dual-link DVI card that can drive the 30" at 2560x1600, and a sound card with optical audio output (unless your computer already has one).
For the video card, look at the ATI Radeon 9600 Pro PC & Mac Edition ($199, AGP 8x) or the Matrox Parhelia DL256 PCI graphics card (about $699, PCI, PCI-X).
The monitor is smaller than 37", but it is less expensive ($2499), has better resolution, can be wall mounted, and will work with the media center PC you currently have. You will take hits on input flexibility and screen size, but if your media center is already handling all of your video needs, all you need is an optical connection from your PC to a good amp to handle your audio.
It all depends on what is most important to you -- a computing experience, broadcast/DVD quality, or lowest cost possible with compromises made all around.