Almost any HDMI male-to-male cable will work. Don't fall for those scammers charging $30 for a HDMI cable.
If you can get a HDMI cable for $1.20, go for it! Maybe pick up a few for that price.
The HP Pavilion G6-2236TX will give much better performance in games, however, neither of these laptops will be able to play modern games on high settings at reasonable framerates.