I think the obvious choice for a bank is computer memory chips. This implies that the sound has been digitized of course. It may be possible to store a sound in a bucket brigade chip or group of chips, but I wouldn't recommend this in light of the cost and availability of memory chips.
Since computer memory is the most convenient medium, using a computer to do the work of storing and fetching the sounds makes sense. So, it might be reasonable to simply use a PC, perhaps running Linux for maximum control of timing and stuff. The beauty of such an approach is that all the hardware is already done for you (PC, soundcard, computer speakers etc)