First Build: Looking for Compatibility and Advice

Hello all! I'm new here so pardon any errors:

I want to build my first computer this summer, but I don't want buy the wrong parts and/or have too many problems. So what I want to know is if all the parts (listed below) would work together. Also, if you have any advice or can suggest a different part that would fit/work better, than please do so.

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I will be attaching this computer to my TV, which is an old Toshiba Projector Television, so I can play games on the TV or just watch Internet videos. I will control it with a wireless keyboard and mouse.

Approximate Purchase Date: This summer
Budget Range: Less than $1000 would be nice
System Usage from Most to Least Important: Gaming (GTR2 mostly), Media (Internet)
Parts Not Required: Graphics Card
Preferred Website(s) for Parts: newegg.com
Country of Origin: USA
Parts Preferences: by brand or type: Don't want to use an AMD processor
Overclocking: Probably not
SLI or Crossfire: Maybe, if I find that I need it.
Monitor Resolution: No idea
Additional Comments: I already have a Graphics card (listed below)

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Parts list:

CPU: Intel Core i5-2500K
Motherboard: Asus Sabertooth P67 —If you can think of a better Motherboard, suggest one, but please explain why it would be better.
PSU:CORSAIR Enthusiast Series CMPSU-650TX 650W —I want to know if this will be enough...
Case: Antec One Hundred Black ATX
Fan/Cooling: Zalman CNPS5X SZ 92mm —If I use the motherboard listed above, then it will need a fan.
RAM: G.SKILL Ripjaws Series 4GB (2 x 2GB) 240-Pin DDR3 SDRAM
Hard drive: Western Digital Caviar Blue 500 GB
CD/DVD: Samsung CD/DVD
Graphics Card: HIS Radeon 2600 XT 512 MB —I already have this card
Other: Koutech IO-RCM621 Media Card Reader

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Secondary question:

The TV is a Toshiba 42H83, and it has a DVI-D (Dual Link) Female input (which is the 2nd to last one on this image). The graphics card has 2 DVI-I (Dual Link) female connections.

I was wondering if I could use this adapter and this cable to connect the TV & computer without too much loss in quality.


—Thanks in advanced!