In: Physics
On a small scale AA primary cells (used in portable electronic devices)are the least expensive per capacity. On a larger scale for rechargeable there are many variables such as cycle life and maintenance requirements but probably some lithium based chemistry is the right answer.
Yes battery tech is improving all the time.
As far as the storage of renewable energy is concerned , it would not be easy because of high number of battery requirement. It would be better to use such sources of energy directly without storage. Batteries are not long lasting , they have a time period after that they stop working. Some chemicals are also used in the batteries which are harmful for our environment . Well, there are lot of discovery and invention are going on but the product they are making is generally not transferred to market due to their high price and other reason.
Are batteries a good solution for energy storage on a utility scale? Maybe as a marketing exercise but it involves too many rare minerals to be realistic on a global scale. Same reason why its not viable for the majority of transport applications (small, short range commuter vehicles for the super rich not withstanding).
Cryogenic energy storage has much more promise for grid scale applications.