drcampbell's post gives you a bare minimum which might run your load correctly.
The key requirement is that the battery store sufficient energy to serve the required load for the required time.
It would be convenient if batteries were rated in watt hours, but instead they are rated in amp-hours. This is simply the current delivered by the battery times the duration of the current flow, as the battery discharges from 'full' to 'empty'. The devil is in the details of this definition; how do you define 'full' and 'empty', and what current level do you use....
For many storage batteries,'empty' is defined either by a particular open circuit voltage, or by a particular voltage under load. So the battery is 'empty' when the voltage reaches a threshold. You could keep discharging the battery (there is more energy in there) but this may damage the battery.
Batteries have internal resistance, so they deliver less total energy at higher currents. So the amp-hour rating will be at a particular current level. For lead-acid storage batteries, this is usually at the 'C/20' rate, meaning a current that is 1/20 of the amp-hour capacity. If you need to run for only 1 hour than your battery will have a lower effective amp-hour capacity.
In general, deep discharge reduces the life of a battery. So you probably want to have larger than minimum capacity for your load requirements.
With more details, we could probably work through a battery sizing problem.
-Jon