I've long been a proponent of the contraptions that Roku makes to watch TV and movies from the Internet.
Roku devices hook up to your TV either via an HDMI cable or via the old school video/audio cables. They are very user friendly. They are small so they don't take up a lot of room in your TV area (in fact, I have some hanging from the back of our wall-mounted TVs so you don't see them at all.) They are easy to set up. They support tons of channels including favorites like Netflix, HuluPlus, HBOGo, Amazon Video and hundreds more.
Anyway, Gizmodo just did a comparison of Roku to other devices (check it out here: Streaming Device Showdown: Who Wins the Battle for Your TV? ) and the Roku won.
So if you are looking for an easy, inexpensive way to start watching Internet TV/Movies, get yourself a Roku. And if you are looking to get your older mom or dad online, this could be a great way to start.