I would recommend something like the EVGA GTX 750Ti http://www.amazon.com/gp/product/B00IDG3NDY. It's a great performing budget card with low power consumption.
I'll have to agree with the Sapphire R9 270X Toxic http://www.amazon.com/gp/product/B00FLMKREQ. It's the fastest and coolest R9 270X on the market right now. I love the DCUII but the Toxic beats it.
If you want something with a great picture quality and nice performance then go with the QNIX QX2710 Evolution II http://www.amazon.com/gp/product/B00BUI44US. It's a 27", 1440p resolution IPS panel monitor with a gorgeous picture quality and you can even overclock the refresh rate to over 100Hz...
+1 for the i5-4670K http://www.amazon.com/gp/product/B00CO8TBOW. It's definitely the best option right now. It's not much better than the 3570K but for the price it would be silly not to go with the 4670K.
You need to get thermal paste, I wouldn't recommend trying household remedies. You will just end up postponing an inevitable demise of your CPU. Get some Arctic Silver 5 or some IC Diamond.
The EVGA GTX 750Ti 2GB model http://www.amazon.com/gp/product/B00IDG3IDO is a great choice for a GPU under $200. You are looking in the right direction. It's in stock for under $200 or you can order it for less and wait for it to ship in a couple weeks.
Get the ASUS GTX770-DC2OC-2GD5 http://www.amazon.com/gp/product/B00D3F7CFK. It's by far the best card you can get for the money and will run everything you want at max settings.
If you can afford the ASUS GTX780-DC2OC-3GD5 http://www.amazon.com/gp/product/B00DWV3NM6 that would be a faster card...
I'd go with the ASUS GTX 760 DCUII http://www.amazon.com/gp/product/B00DBPKEOI. It's the best 760 for the price and the 760 is the best card in your price range.
The ASUS DCUII is the best cooler on the market, has a custom PCB, and great VRM.