MacBook Air / Pro, which fits these needs better?

I'm currently a PC user, and I'm thinking about switching to Mac. But I'm really having a hard time deciding which Mac to get.

Before I start, I should specify my needs:

- It's going to be my desktop replacement. It stays at home most of the time, but once in a while I need to carry it with me

- Need to run Bootcamp / Windows

- I play games, but not a really serious gamer. I want to run games like Arkham City / Total War: Shogun 2, but I don't need highest settings, probably mid - high.

- I don't have lots of stuff to store, most of them are in external hard drives

At first I thought about getting a MacBook Pro 15" (2011 refurbished model), mainly for the extra graphic card included and better processor. Since I'm afraid the Intel HD Graphic 4000 (2012 MacBook Air) will not be enough even for games at mid level graphic settings. But I keep seeing people refer MacBook Air as a "no-brainer". Does it apply on my case? Thanks!