A 2-gallon tank on a pump is not a storage tank by any means. That size tank is solely to allow the pump switch to operate between the set pressures like 40 to 60 psi. I wouldn't even call a 20-gallon tank on a well pump a "storage tank". As GReynoldsd929 said, if you need storage, you need a cistern or holding tank.
And a better control system for well pumps is the Cycle Stop Valve instead of the standard on-off pressure switch. That system allows a smaller tank and provides a pretty much constant pressure to you house much like city water provides. It also increases the life of your well pump and saves energy to boot. Valveman on this forum is best to answer your question after you describe your wants and needs clear;y.