I've done filming with sounds too.
It is damned hard to find a small (bullet-type) camera which is of reasonable quality. I bought a Sony one for about £150 and it was barely acceptable for a u-tube video. There is a better Sony one for about £750 but I haven't yet got around to getting to try it.
A camcorder will be much better quality and those suction mounts (thanks for the URL!) should work great, but on a long flight you will run out of tape / storage and then the camera stops. I am not aware of a consumer camcorder which can be used minus the media but with a video output i.e. effectively as a high quality webcam.
The last movie I did used a analog to RGB (USB2.0) converter for about £50 which was actually of very high quality (I tested it with my Sony HD cam to make sure).
The sound is easily done by tucking a mike into one's headset, though wiring it to a headset mike plug is a lot neater (does anyone have a circuit for this?? - I believe one needs to attenuate the signal a bit).
Getting rid of reflections ranges from tricky to very tricky. The proper solution - for external scenery movies; not what the OP here is after - is to mount the camera externally but that is then not exactly legal, and does need to be done very carefully because you don't want it to come off and e.g. jam in the elevator...
If anyone is interested I can supply details of what I used, and the URL to the movie. The camera came from dogcamsport.co.uk I think and for all I know I may have listed all the kit here at some time in the past.