My recommended C-size rechargeable battery is the EBL 5000mAh Ni-MH. These are low-discharge cells and will hold their charge for year or more.
Rechargeable batteries have made some real improvements in the last five years. Most notably, you can now get rechargeables that don’t go flat after a couple of months! The technology is called “low self-discharge” and means rechargeable batteries can hold 80% of their charge for a year. Low self-discharge batteries (LSD) NiMH cells were first introduced by Sanyo in their Eneloop AA cells in November 2005. Since then, other battery manufacturers have adopted this technology. Then in 2010, companies like Maha started releasing LSD NiMH cells in C and D sizes.
An alkaline C cell is typically rated for about 8000 mAh, but only at a very low current (around 30 mA). When used at a load of 500 mA (such as flashlight), the capacity of an alkaline drops to about half. Overall, there is no difference is power between the alkaline cells and NiMH.
The only advantage of alkaline cells is now just their shelf life (which is about ten years, with minimal self-discharge).
We recommend the EBL 5000mAh Ni-MH rechargeable C-ssize cells, which are available from Amazon. A set of four cells costs around $17.