Program:
http://www.xsplit.com/
Everyone use it to cast on twitch TV for steaming but u can also record ur gaming session. Bitrate / sound quality / resolution etc... lots of option.
Now for Hardware, (capture video game on console) go with this :
http://www.blackmagic-design.com/products/intensity/
or for less money :
http://www.avermedia.com/product/Pro...il.aspx?Id=530
Both can capture HD with HDMI output (so sound + image)
Of course if ur PC can handle it, u don't need any hardware card to capture a PC video game. For console u need one.