To hopefully clarify a bit...
The 10440s people refer to are special-purpose Lithium-ion rechargeables. They'll make the ITP A3 brighter, potentially cause it overheat, and require special handling and charging for safety reasons. It is essentially the same technology as laptop and cell phone batteries, but less controlled due to not being designed for general use.
Sanyo Eneloops are NiMH rechargeables, and these particular ones are known for their stable output and low-self-discharge properties. They will drain on their own over several months, hence the recommendation to use them only if you use the light often, but are pretty much the best rechargeables for general usage. They have the same handling and charging considerations as other typical NiMH AA/AAA rechargeables -- fairly safe and straightforward.
The Lithium primaries in AAA form that people refer to are from Energizer in the US. They have two versions: Advanced (EA92) and Ultimate (L92). The Ultimate version will last longer in the A3 on high mode, but both versions have very long shelf lives (10+ years), handle temperature extremes well, and don't leak. They have slightly higher voltage but are otherwise a drop-in replacement for alkalines. These are the ones you should use for a standby/backup/emergency light, and you can find them in many stores (Walmart, Target, etc in the US).