Which Arduino to get/use?

justmee:
If I just use the ATmega I will have no power regulator, right?

Of course. You have to add all those bits yourself if you need it.

No idea how much power your display uses; just measure it. Keeping the backlight off wills ave a lot of power as well. The data sheet mentions sleep modes (I was talking about the processor itself), so that should be able to save some more.