You'll need to buy DVD's that say one of a few things. Unfortunately there isn't a labeling standard on DVD's.
16:9
16:9 Enhanced
Anamorhpic Widescreen
Anamorphic Video
Widescreen-Enhanced for 16:9
And so on. Just make sure it has either 16:9, Anaorphic, or Enhaced Widescreen somewhere on the package.
Will watching a news channel with ever-present graphics burn in your RPTV? Yes, but it'll take a while to do so. While the screens are much more resitant to burn in, they will still do it eventually. You're not going to be leaving it on Fox News all day (right?), so I'd bet that by the time it becomes a problem you'll either want to buy a new set, or your current one will be dieing anyway.