Solar battery ?

I found this site http://gardenbot.org/ and gave me an idea. I plant when spring comes around but I wanna start a greenhouse to start them off indoors for a higher chance of success but my problem is that I forget to water a lot of the time. and this takes care of it. but I figured I am already using power to light it why use power to control it. So I figured solar power but then when no light (which will be controlled by the arduino) no arduino to monitor soil moisture and then also wont turn lights back on. so I am gonna need a battery but what I am not sure of is what size solar panel I will need to supply the ardunio and charge the battery when the light are on. Also I am not sure of what size batter I will need to power the arduino when the lights are off for up to 16hr. also I will probably be adding a screen to change lighting time and maybe something else depending on what I come up with while developing it.