Hi I was just wanting to build a basic data-sharing project where two Arduinos share sensor information with each other through a wireless shield like the 'wireless inventors shield' which is the one I prefer. I would just like to know what type of battery and size, will give me the longest battery life, also, if it makes a difference, I'm not sure which sensor I will be using (probably humidity or temp.) All help appreciated in advance.
What you should think of is using as little energy as possible. That is send as little data as possible as seldom as possible and put the arduino in sleep mode in between transmission burst. And remember to turn off the rf as well
Transmit and receive the shield itself uses less than 17ma, so alkaline, 2200mah, AA batteries would give you (2200 / 17 =) 129 hours of life. But as nilton stated if you can put everything to sleep in between sending data then your lifetime is going to be much longer.
Your power usage should be quite low so you should probably consider a solar charger, solar panel, and a 3.7V LiPo battery. Those parts would total to about $30.