The PC in the OP isn't bad at all for a TV gaming rig. With midrange rigs, usually the key to enjoying it longer through the years is to be cognizant of the three things that usually kill performance with some titles : AA, Lighting, and Shadows. Trying to run that stuff at Ultra/Max on every title is not always feasible, so judiciously adjusting those settings down a bit while still leaving things at 1080P is a good idea if things aren't as smooth as you want.
I do corporate IT for law firms and health care, but I also still build gaming boxes for friends as a hobby. Long ago I built them as part of a business, dozens per week for years on end, so you get used to spotting what the best deals are and best practices.
That said, I often find for really budget-minded customers that the best thing to do is start with a used workstation, which has several key advantages :
You get lots of RAM for cheap.
The HDDs are often small or not included, which means you can focus on starting with an SSD, and you can add a big storage drive if you want, or wait until later to do so. This is better than starting with a slow spinning HDD.
The component quality of most big-brand workstations is AWESOME. You very seldom see cheap components on the mobo or psu level. Out of a few hundred that I've installed for various clients over the past few years, issues are incredibly rare.
You get a legal windows license included, which makes upgrading to W10 a snap.
Oh, and price :)
Here's a good example of a cheapo gaming box that I just built out one nearly identical a few weeks back :
http://www.ebay.com/itm/Dell-Precision-T3500-Workstation-Xeon-W3570-QC-3-20GHz-8MB-250G-1944877-/381369837427?hash=item58cb69e773:g:c~0AAOSwjVVV13ZR
http://flash.newegg.com/Product/N82E16814202043?nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-TechBargains-_-na-_-na-_-na&AID=12087162&PID=227502&SID=direct_dealdetail_Newegg+Flash_1119_22928&utm_medium=affiliates&utm_source=afc-TechBargains
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231922
So $453 after rebate, or $473 before for :
Xeon 3.2Ghz (this is akin to the early gen i7s with some minor advantages and a good clock speed. Faster than AMD FX series for most gaming situations even though it's quite old by now. Still, most bottlenecks occur on the GPU unless you have an absolute beast).
12GB RAM
240GB SSD
AMD R290 4GB GPU (not too far behind the Nvidia 970 surprisingly!)
Extremely well made stock 525W PSU
Legal Windows
Just pick your KB, Mouse, HDMI cable, and if desired a gamepad, and you're in the $500ish range (depending on how high you want to spend on that stuff).
There are some negatives of course.
The Precision 3500 mobo doesn't have native USB 3.0, though that can be added in a way that doesn't block the GPU with a PCIe card for around $10.
The case doesn't have a 2.5" bay for the SSD, but as they don't have exposed circuitry or produce notable heat, I just cut some foam or cardboard and tuck it into one of the 3.5" bays. (or you can buy a 3.5 to 2.5 converter for a few bucks)
Upgradability on the CPU tops out with the 3.46Ghz Xeon W3690 6-core 12-thread model, with 12MB L2 Cache. This is fairly awesome even today, but as the top dog for the socket it commands about $200 used, which isn't super cheap.
Anyway, here is someone running a Precision 3500 with an Nvidia 960 (way slower than AMD 290 4GB!), still running Battlefront in Ultra 1080P, it's pretty amazing how stout those Xeons were and still are for modern gaming :
https://www.youtube.com/watch?v=peRKp-BN_9c
Edit : forgot, I had to throw one of these in to get the power going to his 290 : http://www.amazon.com/Express-Supply-Adapter-Converter-Splitter/dp/B00XB7PWB6/ref=sr_1_1?s=electronics&ie=UTF8&qid=1447973607&sr=1-1&keywords=4+pin+molex+to+8+pin+pcie
