We've have a little Archos personal media player which I find great. The screen is bigger than an ipod touch at 7 inches, but still small enough to fit into a handbag.
We wanted it small so we could use it taxis when our toddler is restless. It also has a little stand so you can sit it on front of them on planes etc. and a spare battery attachment.
Also good is that you don't need to change downloaded films into the mp4 format, it will play any movie files as they are.
We have an Archos 6.0 which can store around 80-90 movies, but there are several different brands and sizes around.
Re. headphones, I am ordering a pair of Sony children's headphones off Amazon as I can't find them anywhere in HK!!