You realize that finding GPUs for 200$ is nearly impossible right now, unless you pick a 6500XT which is not worth the money I hope.
https://pcpartpicker.com/list/CgxMcb
I think this is about the cheapest you can get with recent hardware, since I'm not sure how the availability is with older cards. The one you linked isn't available anymore in the US.
I don't know G2a from a side of beef, but you need to be very careful about the authenticity of a Windows license. You could be in for a rude awakening in spite of what you've read or been told.
Generally....
Don't get in a rush. Consider both AMD and Intel.
I did not know Best Buy will assemble parts for you.
Does that mean you would have to buy the parts from Best Buy?
Would they assemble it without Windows, and then you take it home and install Windows yourself, using your G2a license?
Don't know about BestBuy since I'm not from the US, but here in Europe, some online retailers offer assembly services. The most basic on the website I ordered from only requires a mainboard, CPU, cooler, and RAM to do so for the most basic system level; mainboard and CPU if you just want, say, the mainboard to run on the latest BIOS. The highest, most expensive level of assemly is the full system minus GPU, which is what I did due to time constraints; simply lacking the time lately to do a full system assembly myself nowadays. No need for the OS. But any shop should be able to assemble your system without an OS, it's not necessary for stability testing, even.
About the license, unless you buy from a very shady website, they are usually legit. I use one of those myself, though from a different store. They are often refurbished or from prebuilts that weren't sold and then taken apart to salvage whatever they could, including licenses. Just look out for certificates that point to legit sellers, they usually post them on their website somewhere.