I would get a 3570 normal version if you aren't overclocking due to faster clock. The CPU will do fine but won't be as good as the 3570, although it's abit pricey I would say it is worth it. I personally don't like the build quality of the HIS cards, I would get another brand like Asus, Gigabyte or MSI as they are cooler and have better build quality. For gaming HDD a WD caviar black will be faster.
(Note the total might be a little higher if you don't have a Microcenter near you with the chosen CPU)
Few tweaks, since you don't have an SSD I recommend a more powerful HDD like the WD Caviar Black. SSD is ~$100 for 120GB and totally worth if you're able to add one later on, or get one now and then add a storage drive later on. Added a case with front USB 3.0 support. Added a cheaper PSU (Seasonic OEM). Cheaper Sony DVD drive.
To answer your your motherboard/GPU question, yes it's all compatible.
Could push the CPU to to a 3570 but that would go over budget by a bit.