Basically, my desire is to power a fan off of a battery pack, while also having a solar panel fueling the battery. It also needs to be small enough to carry with me. Is this possible? Where might I find such a battery pack? I wouldn't mind using rechargeable AAs as opposed to a single battery.
As kk says, charging systems (like in a car) are designed for exactly that. Lead-acid is kind of heavy to carry. Try something modern like lithium-iron or lithium-ion with a higher energy density (I don't know much about Li-Iron, but I just ordered one for my motorcycle that is a third the weight of lead-acid but with the same high current and longevity etc.)
A solar charger is designed to handle exactly the type of application that you are looking for. This will be available with solar panel vendors. The solar charger has separate connections for both the load as well as the battery. When solar power is available, it will supply power to the load, as well as charge the battery (charging voltage and current presettable as per battery capacity). When solar panel voltage goes below a preset level, the automatic switching circuit will enable the battery to take over. As far as your choice of battery is concerned, rechargable AAs will last only for a few minutes (depending on the power consumed by the fan). The best alternative normally used in portable power packs are sealed lead acid batteries which comes in standard power ratings like 6V 4 Ah (Ampere Hour), 12V 7.2 Ah etc. Choice of Solar Panel, Solar Charger and Battery depends on your fan's DC Voltage rating and the back up time (time you need to run the fan when solar power is not available)
