You can use the controller as a remote, but it doesn't have all the specialized functions. But if you're just interested in watching and pausing from time to time, it's fine.
Any HDMI cable will work equally well. Since the data is digital and not analog, there is no degradation except under extremely long cable runs (like 50 feet or more).http://www.monoprice.com/
is a good place to look. You can get a 6' HDMI cable for about $9 shipped.