I use a couple of Lumix ZS-3s and a Sanyo Xacti HD2000 for videoing gigs.
The Lumixes are cheap, offer nice quality for the money, very nice sound from the internal mics (ie not the bad distortion most PAS cameras offer) and are small and discrete. Replacement higher capacity batteries are cheap to source too. They take nice photos too - to the point that I'll often quite happily leave my SLR at home if I'm feeling lazy. The downside is that I think the newer models now have a maximum of 15mins of continuous video footage and the video quality is obviously not on a par with a dedicated camcorder. Also you might feel vaguely daft holding up what is very clearly a cheap P&S camera to record video, depending on the context.
Given your requirements, I might be tempted to go for a cheap standard definition camcorder second hand so that the editing process won't be hideously slow - if I was buying for a kid, I wouldn't want them losing interest due to jumpy computer playback or while waiting for footage to render. If that isn't an issue, I'd be seriously tempted by an old ZS3 with one of those small tripods used as a handle. Then if he doesn't go for it you have a very capable discrete cam for your gear bag ;o)