Gaming PC with new and left over parts

not a fan of the motherboard...the 780 is borderline good enough and may cause some throttling problems for the cpu. Id at least do a 970 chipset or even a 990 so you could later do a FX 8 core.

You can't re-use the video card, the 6450 is horrible for games, even older ones. You need to put aside another 100 for a video card for sure.
If you can't quite get there for budget, I would remove the aftermarket cooler and use the stock and drop RAM to a single 4 gig stick in favor of a new video card, then get a second 4 gig stick when you can.

I would head over to the system section of the forum and do a search there for your budget amount, you should see quite a few build suggestions.

Honestly , AMD only has one CPU capable for playing latest titles 'as recommended' and that is the FX-8xxx. Normally people buy i5s to have a gaming PC, but in all instances your looking at around $700 for all the 'hardware' costs to meet your goals you outlined. If that is 'way too much' and you only have a 'couple hundred' go PS4 then for as little as $200. It plays GTA V at 1080P High settings 30FPS, which that 'planning to buy' doesn't even meet the recommended to do the same thing as a PS4 http://www.geforce.com/games-applications/pc-games/grand-theft-auto-v/system-requirements .

PS4 also plays MANY titles 1080P @ 60FPS as well, and you always know the game WILL play on your PS4, but with a PC well... you can buy a game and never be able to play it because you don't have the hardware capable to play it.

Laughs. I am so sorry, so many people keep posting on here how they see stuff on Youtube and that is the end all be all truth they wish to believe. I never heard of these guys (new to me) and clicking on their feed shows they seem to be some people in connection with a sort of BestBuy of Canada. So I can't say how 'reliable' or truthful these guys maybe or not (influenced to make sales of current products or such as compared to professional news/trade companies who have specific standards on being unbiased).

That said, I am mainly going off this very accurate http://www.ign.com/wikis/xbox-one/PS4_vs._Xbox_One_Native_Resolutions_and_Framerates (major publisher of all things gaming) other articles I seen on TechRadar, GameSpot, etc. all showing that if all you care about is gaming, the NEXGEN (not PS3 and definitely NOT the Xbox One) provides the following points:

1) Ease of use, anyone can pick up the controller and learn to play as all games only can use the buttons/joystick controls.
2) Price value: For $200-400 you get a 3D!! Blueray player, Wireless Controller, Gamers Heatset AND the PS4 itself, the first three items alone is $200 by itself for a PC.
3) Works EVERYTIME. You ALWAYS know a game sold to a PS4 WILL play on the PS4, PC can NOT say that (try loading GTA V on a Walmart $249 laptop/desktop, yeah not gonna happen), without ANY extra costs for hardware.
4) Like all modern BluRay Players and the like, you now get APPS, so you can watch Hulu, Netflix, etc.and always 'up to date' that it will work. No need to find a 'plugin' or update your Java or such just to watch a movie or check a webpage.
5) With a keyboard mouse attachment, for basic web surfing, FB, Twitch.TV, web email, etc. it does just as fine as any Tablet or cheap off the shelf PC from Walmart

Now downsides are mainly for 're-purposing' the PS4 to do other things, such as I can't scan my photos, can't run Photoshop, certainly can't code CSS that well for my 'games tag' website and so on. Those yes are reasons NOT to get a PS4, but if you spend $200 on a PS4, then grab a tablet for $149 or a laptop for $249, that is alot less then $700+ norm for a desktop PC Gaming system and 1/10th the normal $1500+ price for a PC Laptop for Gaming (again the hardware is the big cost here).

Most of all a PS4 isn't DIY which alot of people here on the forums love to do, even if they 'break something' (oops didn't mean to break that Titan X slot into the Mobo...) they just 'buy another' (yeah you want to pay 2X on that nice video card? Or maybe the Pins you broke on that $400 CPU? ). PS4 can't be customized to the personal preference of the individual like a PC can.

Given those real difference, ask yourself then, given the performance, cost, reliance, and ease to deal with a PS4 as compared to the PC, which is more suited for your needs?

If, as you state, the primary purpose of the machine is gaming, then that's a very solid alternative build. Both chips overclock pretty well also. Below is a side-by-side look at the features and benchmarks, which you see there are pros and cons for either and really, IMHO, they would be a coin toss for the use you plan on putting them to.
http://cpuboss.com/cpus/Intel-Pentium-G3258-vs-AMD-FX-6300

But you cant game without a decent graphics card?

Anyways, do not buy the 3258, it has stuttering issues even when overclocked, the cx600 has cheap chinese capicators. You would be much better off with the build i posted earlier.

For that price that is a good system, although the power supply is not that good. With an nVidia 750 Ti video card it will be a good balanced system. Just make sure you run that thing though a few runs of 3DMark benchmark to make sure it does not crash during load and also run the stress test part of Prime95 to test the CPU and RAM stability.

I would not run a loaded system using the VIP power supply, a lot of people just look for the cheapest power supply even when they spend lots of money on the CPU and video card. What they don't realize is that if the power supply can't supply enough power, the system can shut off, reboot, have voltage fluctuations to the other components, and kill all those other fancy pricy parts.

For a lower power video card, the VIP unit will be OK to use, I would not use a card in that that uses more power than the 750 though.

for your price range this MOBO is great:
https://pcpartpicker.com/part/asrock-motherboard-fm2a88xpro3

has the 88X chipset and room for upgrades later on. Great board! Great Reviews here:
http://www.expertreviews.co.uk/pcs/motherboards/1402723/asrock-fm2a88x-pro3-review

good CPU COOLER: http://www.newegg.com/Product/Product.aspx?Item=N82E16835103107