I think you're better off with building a pc specifically for mining, as you can go full out on video cards and can go quite low with the cpu (you can even use a base Celeron for ex). Save your gaming pc to enjoy your games, you'll get bored of gaming at some moment in life..
And yes, I know that you don't want to go with a specific build, but you're not going to get too far with a normal pc. Also, read as many articles as you can about cryptocurrency. It's going to help!