Arduino Nano or Leonardo - The larger amount of SRAM is needed for a display buffer and fonts.
SDCard reader - Using the SDFat library
Battery holder - For 4 * 1.2V AAA rechargeable batteries. This provides 4.8V which can run the arduino directly. If the power socket was used it would need 7V+ to allow for the voltage regulator.
OLED display - 128x64 pixel, bi-colored for status messages