simple blogs work great with getting approved with adsense. I mean SIMPLE. Be sure the pages ALL have content. They've gotten a lot harder to pass in recent years. If you have to, you can also submit a very simple site, then add your gaming site later, and you'll most likely have no problem. It's the initial computer approval you have to get passed.
Just sign up ad adse dot com. With a US ip, it usually takes me a day, then you stick some ads on and wait for the second approval for traffic, and depending on how much traffic youre sending, it can take as little as a couple hours, and voila you have a fully functional account making bucks.