If money is not a problem I would recommend Apple TV.
Apple TV has the advantage of begin wireless, and as you said, your parents will be able to control it from their seat. This quite useful for watching watching shows, but even better for other things, like looking at pictures on your iPad on the big screen, for example.
On the intuitiveness, if your parents already know how to access the multitasking bar at the bottom of the iPad it is pretty easy: just a switch away. Practically speaking, easier than dealing with walking, plugging it in, and having to stand up to input things to the iPad, or dealing with a long cord.
Apple TV has many other advantages/features: Photo Stream through iCloud, Netflix, Youtube, flickr, Internet Radio, WSJ, Movie Rentals, TV Show Store, etc. I don't know how many would your parents use/need, and of course Movies and Shows come for an extra cost, but its something to keep a thought on.
It's $40 dollars more expensive though. If your parents don't need such features, they don't mind a cord, and if they don't really need controlling their iPad while displaying something on the big screen, than it's some good $40 to save, but if you can spare it I think you get plenty of extra features and wireless commodity from it.
Best Answer
The Apple TV 2 is the earliest Apple TV that supports AirPlay Mirroring, being the earliest Apple TV capable of installing Software Update 4.4, which added the feature.
https://support.apple.com/kb/HT202157