powering an Arduino pro mini on battery for months

Just wondering what the best power source for a remote Auduino Pro Mini would be. I’d like the battery to be something small, like a 9 volt battery, but would a group of AA’s be better? Do I just need to find the batteries with the largest mAh rating?

This application may make use of a 434 radio transmitter and it would transmit very infrequently, as in, 1 transmission of a byte or so every few hours to a few days.

A group of AAs will have MUCH higher capacity than a 9V battery.