I have a potable DVD player which I have hooked up to my pi to use as a screen/casing.
What's the best way to power this 12v/1.25A DVD player and my pi from the same power lead or rechargeable battery?
I guess the best way to power that setup is to get a power supply that can deliver both 12V and 5V rails. By any chance, if you have an old usb-to-ide enclosure for 3.5in hdds you'll be in luck because the power supply that comes with it has both. Or you can DIY an old pc power supply to serve the purpose.