The battery that ships with the official battery or a third-party version. The other option is to go with something along the lines of Nyko's Charger Grip ($30 street price), which is designed to improve the PSP's ergonomics and provide an extra five hours of life from its built-in lithium-ion rechargeable battery.
The device itself is partially collapsible when not in use, and it's made of lightweight plastic. That's good, because it adds little weight to the PSP, but it does feel a tad flimsy. With some finessing, you clip your PSP into the Charger Grip, and in a matter of moments, your PSP will suddenly look and feel a whole lot more like a standard . If we had a criticism for the Charger Grip, it's that its plastic clips may be susceptible to breaking, especially if someone should accidentally step on the accessory (or some other form of force is brought to bear on its plastic extensions). Otherwise, the Charger Grip works as advertised. Because of the Nyko's shape, your hand will feel less cramped when playing with the PSP for long periods. Naturally, as with any controller, it's best to take breaks from time to time and do a little stretching or your hand will cramp, regardless.
To juice the device, you use the charger that came with your PSP. It takes about the same amount of time to fully replenish the Charger Grip as it does to charge the battery in your PSP--we did it in a little more than two hours. The Charger Grip comes with a little external power cord that you plug into the power jack on your PSP, and Nyko has carved a little indentation into the plastic on the left handle so that you can plug in a pair of headphones. That said, some bulkier headphone jacks won't fit. For instance, we couldn't plug in a pair of earbuds. Aside from that glitch, however, the Charger Grip is a good solution for those looking for both a backup battery and improved ergonomics for their PSP.