14500 Li-ion battery 3.7V (4.2V full), most are 700-800 mAh. (1600mAh 14500 is fake, or over-rated)
Rechargeable Eneloop AA is 1.2V, 1900-2200 mAh,
Circuit protection is important, especially for Li-ions, if someone forgets to turn off the light, the battery will keep draining, maybe to 0V, and dead.
Suggested 14500 battery: keeppower, efest, xtar.
Built-in USB battery, is usually longer. An independent charger is more suggested...