mrShrimp:
Ok, it seems like I will have to use an SD card. I definitely do not trust myself to make this from scratch, so would I be able to start with something like this: MicroSD card breakout board+ : ID 254 : Adafruit Industries, Unique & fun DIY electronics and kits, and interface it to a standalone ATmega328?
Yes and the tutorials and example available from Adafruit are usually a worthwhile read, the only thing to keep in mind is you won't have the luxuary of labeled headers. If you go the standalone ATmega328 route, save yourself some time and effort and get one with the Arduino bootloader pre-installed. Unless of course you want to learn how to use ICSP to either load the Arduino bootloader on a blank chip or program the ATmega328 using a different programming tool chain than the Arduino IDE.