You're best bet is to decide between 2 possible options:
1. 2 AW brand protected RCR123 size 3.7V Li-Ion cells. These have a label capacity of 750mAH but will perform closer to the 600mAH mentioned previously. These are good quality cells that have safety features other brands may or may not have. They are very much worth the money. By going this route, your light will run about half as long as it does on 2xCR123 primary cells, but will stay at full brightness through the entire run.
2. 1 17670 size protected AW brand 3.7V Li-Ion cell. This cell has a label capacity of 1600mAH and comes very close to this rating under the loads involved here. However, because you will have a lower input voltage than the 2xCR123 configuration, the LED module will draw a little more current to overcome the deficiency, also, the P60L uses a "buck" style regulation circuitry, meaning that it requires the input voltage to be above the Vf of the LED to stay in regulation. The single 17670 cell will fall below the Vf of the LED at some point during the discharge, which will have the effect of a slowly diminishing output, and the advantage of very stretched out runtimes when you need it.
Both options are a tradeoff but will work well. In either case, I highly recommend buying good quality protected Li-ion cells, this is why I suggest AW brand cells. There are numerous safety issues surrounding Li-Ion cells, by using a quality protected cell, you don't *need* to have nearly as in-depth an understanding of Li-Ion cells. It would still be worth taking the time to do some research so you can use the cells in the safest most rewarding manner possible.
You can buy AW brand cells from lighthound.com or directly from AW through his sales thread in the dealer section of the CPF marketplace. As far as the charger is concerned. If you are willing, a Pila ICB is one of the best out there and actually terminates the charging correctly. I have seen them as low as ~$37, if that's too much... You can get by using something like a DSD or Ultrafire wf-139.