Depending on what size screen you want you can fit 3 decent length movies on a 1gb MP4 player, you have to convert the file to a special format (to suit the screen resolution hence films take so little space) but I brought a load of these things as presents for kids at christmas they were £15 each and had a 1.8" screen, I think they do them in 8gb as well for about £35 over here. Its hard to recommend brand names across the globe as often these things are rebranded by a dozen different companies. The ones I got were "stage" brand, and the first one I got to test them has put up with being in my pockets with my keys and being generally thrown about for 4-5 months Its still going although the outer casing is well scratched up it works perfectly, surprising for something so cheap.
I did try a bigger one also by stage brand but a different design with a 2.5" screen which lasted 2 weeks in my pockets
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This is the player I brought :-
http://www.ebuyer.com/product/134590
there is an 8gb version here if you want to put over 25 films on a player.
http://www.ebuyer.com/product/144952
They are available in a range of colours. The head phones which come with them are pretty poor I dont know if a built in decent sound is a must or if head phones are ok for your daughter.