Let the hive mind of Engadget get that for you.
"We need a digital camera that can be switched on and fire off that first shot fast. It's not a commonly tracked statistic on any review site, and nobody seems to have this information for every camera. We were hoping other readers could inform us as to what small digital cameras can fire off their first pics in under a second (ideally under half a second). It needs to be small, but mostly, just really quick in operation. Thanks!"
Trying to compete with the Nano is a bad idea. As has been previously mentioned, iPod has the name going for it, in the same way that Walkman did for radios/tape decks. The player could also be made out of magical gold and have 100Gb of storage, but the price and SonicStage would still kill it, unfortunately. Right now, SanDisk Sansa players are the only DAP that can come close to "competing" with the iPod.