The most common types of storage batteries are lead-acid, lithium-ion, and nickel-cadmium batteries.  Lead-acid is the oldest and most used type, they’re typically found in cars and other vehicles.  These ones aren’t too pricey but they do have a couple downfalls;  they don’t last long and require regular maintenance.
Lithium-ion batteries on the other hand cost a bit more money but offer longer lifespans, faster charging times and higher energy densities.  These ones are commonly found in smartphones, laptops and electric vehicles.