You seem to have started at the wrong end.
First you set up your arduino and sensors then you measure the current and find out how much you use in an hour.
Times by 24 hours and there is your current to run your arduino for a day.
Rule of thumb is allow for 3 days without sun and there is your battery capacity.
Remember if you do not want to damage your battery never discharge it below the recomended amount.
Eg. A deep cycle lead acid is around 60% discharge (Check the battery specs) so if you have a 10 Amp hour battery you should only use 6 amps before recharging.
For charging from a solar panel you should allow about 6 hours of full sun on a good day as your recharge so you would need one amp for 6 hours from the panel to recharge your battery.
Remember you will be working on 6 hours of sun to replace up to 72 hours (3 days) of use!
There is a lot more involved but that should get you started.
Daz