xl97:
Each pin on an Arduino can only give (roughly) 20mA... some say up to 40mA max..
Read the data sheet of the ATmega328 processor: it can produce 20 mA per pin continuous, absolute maximum rating is 40 mA.
With a total or around 100-150mA or so I have read for the whole board. (limit)
That depends highly on how you power the board and how you draw the power from the board.
justmee:
I want to build a battery-saving system - so what is my best pick here? The LCDs use 3.3V but can operate with 5V too.
A barebones ATmega processor. Use the Arduino board for prototyping, then the final project on just a processor with minimal peripherals. Use the sleep modes for additional power saving.
Note that LCD screens themselves tend to use so much power that the savings by not using a development board may be negligible. A Pro Mini board has the fewest extra components (do get rid of that power LED) so will give you the easiest route to a low power system.