I recently received the iPod Touch as a gift and have found it quite convenient for watching videos, particularly when it saves me the trouble of getting my laptop and all the assorted cables out on shorter flights. You can watch right up until they close the door, then keep it in a pocket til you reach 10,000 ft!

The Apple Store has a number of cases and screen protectors - the latter will avoid the fingerprint problem to which you're referring, although you have to make sure not to get any lint underneath the protector. I have the Griffin Elan Form and have been happy with the case (leather outside, hard poly inside). It came with a screen protector that came with some lint on it, so I still have a couple bubbles, but don't really notice them anymore. There are separate screen protectors you can get that may be better.

I got the 8 GB model, which is a bit too small for carrying lots of videos along with your entire iTunes library - I'd recommend one of the larger ones. As for battery life, you can get the iPod iTip and hook it up to your iGo for longer flights if necessary.