Should i buy a gaming PC or just build one?

You should build the gaming pc because cost low than buying one.A nice gaming pc cost about $400 but buying new one will cost you about $600. You should buy part in newegg.com because it cost low.

Well if you buy that configuration you picked, be prepare to run BF4 at low settings with 10 FPS, the principal component on PC gaming is the graphics card, you selected an onboard graphics card which I think is like intel HD 4000 graphics, so no, you won't like the performance of this PC.

Building a PC is often better than buying a pre-built one, some months ago, I wanted a gaming desktop and I did some research and I found the Dell XPS 8700 and it had a core i7 4770 CPU and a GTX 660, it's great and all, I can play BF4 at ultra settings with 60+FPS without anti-aliasing, but I regret it, it costs like $1500, I could've saved like $200-$300 if I would've build it myself.
Building one is very easy, the hard part is to choose which components to add to your rig, just be sure to have at least these specs if you want to have a good experience at games:

CPU: a core i5/i7 4-core CPU with +3.0Ghz of speed, be sure to also buy a CPU cooler

RAM: 8GB is more than enough for gaming

HDD: A 1TB 7200RPM hard drive, a 5400RPM one would also be good.

Case: One that supports ATX and micro-ATX motherboard and that at least have a fan, if you want to go big, go with a full-tower case, just be careful because they are pretty big

GPU: If you want it from Nvidia go with the GTX 650, you could have a good experience with this card in games, if you want it from AMD go with the Radeon HD 7850 or 7870, also really good performance

PSU: A 600W, 80 plus certified PSU that has at least 36 amps on the +12Vrail and has at least x2 2+6 PCI-e power connectors, be sure to buy it from corsair or XFX

Motherboard: A micro-ATX or just a ATX LGA 1155 mobo, with at least one PCI express X16 slot., be sure that is supports Core i5 CPU's

Cooling: This is your choice, you can go with standard air fans which are easy to install but they won't cool down your PC a lot, or liquid cooling, which will cool down your PC a lot but it's kind of difficult to install

The other PC parts like the CD drives or sound cards or other cooling methods are up to you

Keep saving your money and build a better system. If you bought that one, you would be disappointed. Save at least $400 more and build something with at least a 4th generation i5 (Haswell) in it. The motherboard would have to have an 1150 socket to support the Haswell processors but you would be future-proofing your system by allowing the chance to upgrade to a faster CPU down the road. 1155 socket boards are on their way out the door so I'd advise against buying one of those.

Start watching YouTube tutorial videos on how to build your own PC to learn how. If you've never built one, ever, and find the task too daunting, then I'd recruit a friend who has and you will save yourself a ton of money. If you go with building it yourself, be sure to get an ESD anti-static wrist strap to prevent zapping your new parts with a static shock that will render it one expensive paperweight.