You need to decide/discover/guess what voltage and current you need to drive your motor, as the first step.
2 AA batteries only gives you around 3V to play with (assuming they're conventional domestic batteries) and not much current. With the supply voltage this low you may have trouble driving through an H-bridge because the voltage drop across the H-bridge would become significant. If that's a problem then you would need to either increase the voltage supplied by your batteries, or increase the current and use a DC-DC converter to step the voltage up. Whether you need a converter and if so which one you need depends completely on what voltage and current your motor requires and what voltage and current you can get from your batteries.
There are very many H-bridge drivers suitable for low voltage low current motors, and you can use whichever one you like which has the required electrical spec. If the driver is packages as a shield, you can use any Arduino that is compatible with that shield. There are also clones such as the Baby Orangutan which has an integral H-bridge driver which would be capable of dealing with motors drawing a few tenths of an amp, which is probably sufficient for a motor suitable to be powered by a couple of AA cells.