It would be better/faster to simply use an ethernet cable to connect it to your cable modem or router, but if that's not possible, then something like this should work.
There ARE cheaper ones, but when it comes to wireless adapters, much like wireless routers, you pretty much get what you pay for and cheap adapters give you cheap signal quality. So, any USB 3.0 wireless N or AC adapter will work, but this would probably be the lowest end unit I'd buy for my own self, although unless it was a mobile device I'd just run Ethernet cable to it as it's much faster, more reliable and won't cut out or drop signal strength, ever.
PCPartPicker part list /
Price breakdown by merchant
Wireless Network Adapter: TP-Link - Archer T4UH USB 3.0 802.11a/b/g/n/ac Wi-Fi Adapter ($29.99 @ Amazon)
Total: $29.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-01-20 22:14 EST-0500
I REALLY think that calling that a "gaming" system is QUITE the stretch though. It's got a five or six year old FX processor and a VERY low end graphics card. In reality, that system isn't much more than a basic business machine or internet browser, although you will be able to play very low demand games or pretty much any kind of online, in browser games. It will not play any real PC games though unless you are willing to turn every possible setting down to it's lowest setting, and even then it would be crappy and almost not enjoyable.
Perfectly fine for basic internet and application use though.