Do not confuse reality and commercial ads, please
So-called "energizer lithium" alkaline batteries are still
non-rechargeable alkaline 1,5V batteries ..... where instead "real" Organic Lithium, Lithium-Ion or Lithium-Polymer batteries are 3V (primary) or 3,7V (rechargeable) batteries .....
About alkaline rechargeable batteries, these are a relatively old technology (1998, if i recall correctly), used for produce standard cell-sized
alkaline-manganese dioxide batteries that can be recharged til some hundred of times (it depend from how much current you take from them in the discharge cycles, and how much last of the charge in the cell, when you recharge it) .....
Some of them are commercialized as BIGRam and Alcava, and more recently EnviroCell and GrandCell (there are other producers, but i don't know all them, and some of them does not import here)
The "best" only depend from your host type and use.