How much battery power will my Arduino need?
Plan A would be to identify the make and model of each item, find it's data sheet, look up power used by each item (at start-up, active, idle etc) add them up and from that work out what sort of current you need and decide how long you want to run it from batteries. From that you can find a suitable battery. 

Plan B would be to plug it into a bench supply and measure current draw under various conditions.