The inexpensive Roku Express almost appears to be a no-brainer as either a cheap intro to the world of streaming video, or as a sweet addition for that second TV that you have been meaning to hook up.
At around $30, that is a great price point - I would try almost anything for $30! It even comes with an HDMI cable. My only two (slight) reservations are that it connects via Wi-Fi only, and it has an infrared remote (rather than the Bluetooth one).
I personally have a thing against streaming video over Wi-Fi, and we have a Roku model that has an IR remote. That is about the only thing I dislike about our Roku; you have to be a bit of a sharpshooter to use that thing.
Still, a very well-priced product for most of us.