I had a look at the jaycar cameras. IMHO this is not the the best option.
Most, as you said, have a video out & you have to convert this. I suspect control of shutter speed and other things like gain will be poor to non existent for these cameras.
The basic Web cams have a myriad of software controls that make them more suitable for your needs. I know the old ToUcam is no longer available but I suspect there are many suitable web-cams are out there, indeed
new ones, that have better resolution than the old ToUcam.
You just need to research & trawl the net. Try these links,
here and
here here.