For the Rasberry Pi board running at 5v you can use a voltage regulator such as the LM7805, this will give a constant voltage output at 5v, this will deliver up to 1 amp which should be plenty for your board, does it say if the current rating is R.M.S?
You would connect the regulator with positive to positive, ground to ground and the output pin will be 5v
You can use a resistor to resist the current flowing through the circuit as well as placing a smoothing capacitor in parallel with your power supply to reduce fluctuations.
Similarly you can regulate a 12v supply through a regulator as above (or you can use a zener diode http://www.reuk.co.uk/What-is-.....-Diode.htm
) , although a screen might pull a bit more than 1 amp so look for one with the right current rating. (depending on your source you might not need to regulate the supply)
Have you had a look at laptop batteries? You can seem to get ones with a damn good capacity for not that much money, the more mAh the better.
You might also want to consider adding a cooling fan if your putting the board in an enclosed box, you can use either your 12v or 5v supply.
Hope this helps your project.