Good decision to get her her own seat. My kids would get that "car seat mentality" where they're just expecting to be sitting strapped in like a car. The one time (only once!) that we held DD on our lap, it was terrible, she was all over the place.
We have an 8" Poloroid and it's been great. I agree with a previous poster about checking the battery life beforehand so you know what to expect, and possibly getting a second battery. I would also recommend the service plan with a device like this. Our first player didn't work very well and
Best Buy wound up just replacing it with a better model for no cost.
We have always used headphones with ours (get a player with 2 headphone jacks so you can listen, too, or for future kids!). When our kids were too little to wear them, I'd hang the headphones around their neck and turn up the volume so they could still hear. I've found that airplanes are so loud from the engines that the kids couldn't hear the DVD player even turned all the way up unless I did this headphone trick. I have bought "kid-size" headphones at Target, but again at such a young age, they wouldn't keep them on.
I also agree about the screen that rotates around, not only to keep the buttons away but just to get the screen closer. A laptop is also a good idea if you have one.
We took our DVD player to Sweden with us last summer, and it was a blessing during many times sitting and waiting for ferries, trains, etc. At one point on a 3-hour ferry ride, some Swedish children came over and sat down next to my kids and nieces and watched the movie with them!