If you want to overclock the cpu, you need to change the motheboard to a Z77 motherboard, and probably get the Seasonic S12II 520 PSU as well. If you're not going to overclock the cpu, I suggest getting something cheaper like the i5-3470 which provides almost similar performance.
You didn't mention what this computer is for or how big a concern you have for the budget.
This is a cpu heavy build. You seam like you are looking to save money, you may want to opt for a cheaper cpu, in that case you could also save on the motherboard by getting one with a cheaper chipset.
The other route would be to get a more expensive GPU to match the rest.
That is a great deal on a case, but, if it is a concern, I would look to get on with USB 3.0 ports as the motherboard has USB 3.0 Headers or get a drive bay adapter that has USB 3.0 ports. There was a little confusion in your part selection, as EzioAs said, about overclocking. I left it out but you need to get a Z77 motherboard if you plan to do so. For this budget, though, I wouldn't worry about overclocking. If you plan on adding another GPU later, you need to get at least a 650W PSU.
I'll be using this primarily for gaming and some video editing in Sony Vegas Pro, After Effects CS5, and Photoshop CS5. I actually won't be overclocking so I'll just go for a 3470. As for the 7870, is it really worth the price jump from a 7850? Will I be fine running on a stock cooler with the i5 as long as I'm running on stock speeds? As for the price I would like it to be $500-$600, preferably as close to $500 as possible.
Stock coolers are fine even for a "K" cpu as long as you're not overclocking. I really recommend you change that though because they're loud and they use plastic push pins. The CM Hyper 212 is a good replacement or the TX3 which is cheaper but still better than the stock cooler