Recording game chat is fairly simple and any capture device can do it , all you need to do is set your preferences on your xbox to allow game chat to go through your speakers or headset and speakers.
As for devices , I started off with the Roxio SD and then moved on to the Roxio HD. I'd recommend neither though as I'm currently using an Elgato which ( if the recording program is open ) allows you to go back and record things that you might have missed.
If you could afford it though and your PC/laptop could handle it , I'd recommend getting a black magic capture card as they're the best in the business.But they are't cheap.