This is the battery I chose to use; it's available at http://www.all-battery.com/li-ion1865037v2600mahrechargeablebatterieswithpcb-1.aspx
. It's a single-cell lithium-ion battery with a nominal voltage of 3.7V and a rated capacity of 2600mAh. What makes this battery fairly unique is that (as can be seen in the picture) there's a small round PCB underneath the plastic sleeve of the battery, which contains an IC that protects the battery against severe overcharge or over-discharge. If the battery voltage drops below 2.5V, the IC disconnects the battery from the load and will only reset when a charging current is detected; if the cell voltage reaches 4.25V the charge current will be shut off until a load current discharges the battery somewhat. Unfortunately these thresholds only protect against severe mistreatment -- they allow moderate abuse to the battery which can pretty quickly shorten the life of the battery. I'd like to find a self-protected battery that keeps itself better protected, say with thresholds of 3.0V and 4.0V, but it doesn't seem like there's anything available.
Because of the embedded PCB, it's not a wise idea to solder directly to the battery (and anyhow that's a lot of heat for a Li-ion battery), so I sprang for a battery holder, and soldered to the leads of the holder instead of directly to the battery.