I would consider this to be the minimum laptop you would want to buy.http://www.newegg.com/Product/Product.aspx?Item=N82E16834230216
Games need both processing and graphics power although they rely more heavily on the graphics card. Just a processor will not play many games besides facebook games.
This laptop has a graphics card build into the processor and then another separate. Although it is refurbished I wouldn't worry too much ASUS is know to be one of the best laptop companies.