Refinishing basement and want to create a home Theatre; beginner on a Budget (1 Viewer)

The space is 18 ft wide by 20 ft deep
My desired screen size is 109 diagonal inches and I'd like a HD quality image from my projector.
I plan on an AV Receiver
The other components at play are:
DirectTV HDMI
Xbox 360 HDMI
Wii not sure on wiring to projector
Apple TV HDMI
Blu Ray player HDMI
apple computer HDMI
The room is small enough where I can get away with a 5.1 channel surround sound system.
My questions are;
What components need to be visible and which ones can I hide?
How many HDMI cables can be run through A receiver?
If the receiver is hidden 15 feet away from the screen and 8 feet away from the projector how much HDMI cable am I going to need?
What type of HD projector is going to give me an HD quality picture on a 109' diagonal screen and how far back will the projector be from the screen?
Thank you in advance for your help.
TKMorris

My desired screen size is 109 diagonal inches and I'd like a HD quality image from my projector.

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What's your seating distance? http://myhometheater.homestead.com/viewingdistancecalculator.html

What components need to be visible and which ones can I hide?

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You can't hide a projector. Other than that, it's up to you. I've seen game systems where the only thing visible were the controllers.

How many HDMI cables can be run through A receiver?

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If you buy a receiver with 4 HDMI inputs, then 4. If you need more, you can also add an HDMI switch box. My projector only has 1 HDMI input and I connect 4 HDMI components directly to it. My receiver doesn't support HDMI.

If the receiver is hidden 15 feet away from the screen and 8 feet away from the projector how much HDMI cable am I going to need?

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The distance between the screen and the receiver is irrelevant. Is the 8 feet as the "crow flies" or is that taking into account hiding the wires? My equipment rack is about 4 feet from my projector but I have a 35 foot HDMI cable because I run the cable through the wall and attic before reaching my projector.

What type of HD projector is going to give me an HD quality picture on a 109' diagonal screen

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One that has an HD resolution. Whether or not you perceive it to be high def will depend on your seating distance.

how far back will the projector be from the screen?

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Depends on the projector. My Panasonic can range from 12 feet to 30 feet for my 103" screen. There's a throw distance calculator at Projector Central that programmed for almost every projector they carry.