($140) Hard Drive: Samsung Spinpoint F3. Unfortunately hard drive prices have skyrocketed since the flooding (this drive was $60 a month ago), but this is the sweet spot for price, performance, and size. It's 1TB and 7200RPM and it's very quiet. http://www.newegg.com/Product/Product.aspx?Item=N82E168...
($50) RAM: Whatever 8GB 2x4GB kit is cheapest at the time. RAM prices fluctuate often so I'm not going to list a particular kit, but anything from the following list will be great (1600mhz, 1.5V, CAS Latency 9): http://www.newegg.com/Product/ProductList.aspx?Submit=E...
I would go with the cheapest thing on that list from either Corsair, G.Skill, Mushkin, or Kingston.
($65) PSU: About ~550W from Corsair, Antec, or Seasonic. You don't need a whole lot to power this system and 550W will be enough. Brand matters for power supplies and Antec, Corsair, and Seasonic are going to give the best efficiency and the most reliability. The cheapest model I found that fits the bill is the following Antec unit: http://www.newegg.com/Product/Product.aspx?Item=N82E168...
At this point you're at about $900. If you want to fill out your budget you've got the following choices:
(1) Replace the i5-2500k with an i7-2600k. The 2600k has hyperthreading which helps in multithreaded applications. I don't recommend this option.
(2) Replace the 560ti with a better card. A 2GB 6950 or 6970 would be a nice upgrade. This is what I would do.
(3) Add an SSD to the build. These are relatively expensive but worth it. An SSD is a smaller drive (I'd recommend about $200 for 120GB) that is very fast and you install your OS on it. $200 is a lot for a 120GB hard drive, but there is no bigger performance upgrade for the price.
If you want to do any of those things, let me know and I'll give some recommendations.
Tack on a little sales tax and Bobs your uncle under 1200. You may want to go
a little bigger on the power supply for head room in case you go SLI in the future or simply get a more demanding GPU all together.
Just my 2 cents do with it what you will.