Because your build is not for gaming but more for video playback etc.... and within the confines of your list I would choose the following
Motherboard: Gigabyte GA-Z68XP-UD4 $220
CPU: Core i5 2500 $220
Case: ThermalTake V3 $76
Opt.Dr.: LG Blu-Ray Reader$69
HDD: Seagate Barracuda 500GB $80
Ram: Crucial Ballistix Sport 1600mhz ddr3 $45
GPU: MSI 1GB GTX560OC Ti [x16] $269
As andrew stated you would need a power supply unit as well. a 600w 80+ efficient psu from a vendor like Antec,Corsair,Silverstone,or seasonic would be the best choices and a modular one would keep you from having a mess of cables.
Now the reason I chose the other components.
I chose the mobo because it has an extra slot in case you want to sli(double up your graphics cards) for better performance. I also think it is the better choice for your video application as it has the z68 chipset which allows the system to choose the most adequate graphics between your card and your processor and while using one gives the other a break.
The processor I chose because of the choices available it is the best for video editing. The amd 8 core is also good but I would never CHOOSE Amd over Intel if given a choice. For that price tho I would get a 2500k overclockable for a few bucks less. lol
I chose the case because it is cost efficient ,sturdy and has good connectivity,again keeping the reason for the build in mind.
I chose the blue ray drive because with a movie oriented machine it only makes sence
I chose the hdd because seagate is a good product and while smaller than the other drives more worth the price. 500g is after all a lot of space and you can always add another one later if needed
while ram is listed there were no choices so I made my own and added the price. I chose it because I have used it in more than 10 builds and I have never had a problem with it. A good product and a good price
I chose the graphics card(GPU) because it was the only nvidea card listed and after twenty + builds under my belt, I have never had an issue with nvidea. The amd (radeon cards can be good and even out perform nvidea sometimes, but they have alot of issues with their oper. software called Catalyst. I have had problems with 5 out of 6 radeon builds. 4 of the six I ended up returning the gpu and getting nvidea
Lastly I would think you could find a power supply(PSU) for around $80 that is within my perameters listed above ,putting the total cost of the build @ $1059 however the prices listed for your components is way to much and this build should only cost about $850-$950 putting it well within your hypothetical budget.
That being said, I would save money on the mobo and get this for the better warrantee and many great features and overclocking stability and for the on board soundblaster for better movie experience.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131759
I would for the same money get the i5-2500k processor for overclocking ability
I would not choose such an expensive gpu and one like this should serve the build well
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121446
However I realize that you are not really going to build this and the choices are hypothetical so I picked parts from the list and explained for you why I picked each part. I hope it helps you with your quandery,