buying a gaming rig to mine is overkill. it will have a much stronger cpu than needed as well as more storage and more ram than needed.
if you do want to go that route though make sure it can take at least two video cards (with good spacing between them) and have the cooling and psu power (with extra peg connectors) to handle 300-400+ watts of video cards. like 1080(ti)s.
plenty of guides here to make cheap miners for a fraction of the cost of a "gaming" rig.
of course if your primary goal is to game and make a little coin on the side, go for the gaming rig.
I guess it would be a good to go with the gaming PC option if you're just looking into it for testing and as a hobby, if it doesn't really work out, you indeed still have the gaming pc. Whereas if you had just built a dedicated mining rig, you'd be at a total loss if you decided that mining wasn't for you.
One other thing though, how much value does it really retain as a gaming pc after you've used it for mining for, say, a year or more?