Like anywaypasible says, having a home theater PC is certainly a plus, but as you suggest, it's a lot cheaper to just run an HDMI and USB cable through the wall and using your current PC (in the other room) for storing your music and video libraries. There are customizable wall plates at most home improvement stores for running network, HDMI, USB, and PS2 cables through the walls.
With that in place, you only need some way to control the PC. Personally, I use this Microsoft Media Center Remote Control
and this Microsoft Media Center Keyboard
to control my HTPC. Note that the remote control I linked also comes with the IR receiver. This connects via USB (hence the need for the USB wall port) to the PC and allows wireless control of the PC. There are other options, of course. I just linked what I use so you have some idea of what you're going to need.
One more note based on my experience. On a dual monitor setup in extended mode (note sure about clone mode), Windows Media Center will only display on the primary screen. Using my Radeon HD 4670 and Catalyst Control Center, I set up a hotkey to toggle the primary display to get around this.
Next up is either the HDTV or Projector. One of the primary concerns here will be the room dimensions and the seating arrangement. For instance, my living room, where I have my projector set up, is 19' x 12'. With my projector, the 17' throw distance (the distance from the projector lens to the screen) gives me about a 11' screen. Since my projector's maximum resolution is only 1280x724, if I sit much closer than 15', I start to notice the "screen door" effect (example
). With a smaller screen size and/or higher display resolution, you can minimize this effect.
Another concern with a projector is cabling. You need to remember that the projector is on one side of the room and possibly even ceiling mounted, while your speakers are on the other side. Do you really want to run either a video cable or speaker wires the length of your room? If you decide on a ceiling mounted projector, how are you going to get power to it? Are you going to have to run an extension cable across the ceiling and down the wall to a power outlet? If it's not ceiling mounted, is the seating arrangement such that no one sits between the projector and the screen?
Next, there is lighting control. While newer projectors can probably handle ambient light better than my BenQ MP610 projector, I need to get my living room fairly dark when watching movies. Are you able to control the lighting in your room?
Finally, there's cost. Again, a lot depends on your seating arrangement and room dimensions. While you can probably get by with a 720p projector ($500-$800), I'd really recommend going with a 1080p projector ($900-$1200). Add in all the extra costs associated with the projector (screen, lighting control, long cables/wires, etc...), you're pretty much at the limit of your budget and we haven't even discussed the surround sound system yet.
Obviously, just going with a large screen HDTV eliminates most (if not all) of the issues, but even with all the cons towards using a projector, if you can work around them and have the room size to truly enjoy it, I highly recommend going that route.
This is an old image of my living room from before I got the pull down screen. It's just some screen material pinned to the black-out curtains that cover the windows along my 12' wall. Hopefully, you get the idea of what the results can look like.
As far as the surround sound system is concerned, the primary issue is whether or not it does HDMI audio processing; meaning, does the system process and output the audio from an HDMI cable to your speakers or does it just pass it through to the video display. My Onkyo HT-S3300
does not do HDMI audio processing, so I have to run a separate audio cable to the receiver. Since your PC is in the other room, that's something else you need to consider. You'll also need to take into account the number of devices you want to connect (HTPC, Blu-Ray, etc) and how they're connected (HDMI, Component, etc...).
Given the strict budget of $1500, I'd say a 1080p projector setup is outside of your range. A 720p projector setup is doable, but you may not be 100% happy with the results (I'm about 95% satisfied). A large screen 1080p HDTV setup should be within your budget range and is probably the easiest to set up.
Hope this helps.