Solar storage batteries have traditionally been large deep cycle AGM lead acid batteries. They are relatively inexpensive and have proved to be reliable.  The downside to lead acid batteries is the percent of discharge and the charge rate. Recently, a new battery has emerged that is 1/4 the weight, can be discharged much deeper and can be recharged faster without the fear of warping the plates or gassing the battery. These batteries are referred to as LiFePO4 ( Lithium Iron Phosphate). They are still quite expensive but they are ideal for portable power packs. One of the biggest draw backs to LiFePO4 batteries is that it requires a BMS (battery Management System) to balance the individual cell voltages.