If you want to connect HDMI you could get an HDMIPi and a battrey pack.
There are some cheap 7" TFT screens with HDMI driver boards (about £35) that you could power from a 5V battery pack (officially most are 12V, but I have one that works fone at 5V. You would need to package it.
A good option ight be a cheap tablet.For less than £50
you can get one that will take a TF card and has USB and WiFi. It has a Mali400 GPU which I think should cope with HD video playback.
These things are getting crazy cheap.