Batteries are all roughly the same as far as their efficiency is concerned. They differ in their chemistry and capacity in Ampere hours (Ah) or milliampere hours (mAh).
First you have to decide what your use will be: what voltage and what current will your application circuitry require, and for how long should it run on the battery alone?
Then choose the battery, to provide the required voltage and current, for the desired hours. Then choose the charger/solar cell options.