Picture in, HDMI out
You will, though, need to make sure whichever camcorder you pick can connect up to streaming hardware and software. The best starting point for that is an HDMI connection.
Fortunately most consumer camcorders come with HDMI out; some might have analogue out too, which is a useful bonus. Pro camcorders will use HD-SDI, which is better; but those cameras, and the interfaces they connect to, cost more than HDMI-only ones.
You should check that the HDMI signal outputs in all the resolutions you need, and doesn’t introduce a delay into the signal. You also want to make sure that the camera can output over HDMI without setting information displayed; this is a ‘clean HDMI’ feed. Some camcorders only remove this information on playback, not recording.
Clean HDMI is standard on pro camcorders, and is a feature on most higher-end consumer ones. It is not standard on most DSLRs (save for full-frame ones, such as the Canon 5D mk III and the Nikon D800, although Nikon is adding it to more and more of its lower end models; it is also available on the Panasonic GH4). You should also check if the camera can continue to send an image over HDMI without going into a power saving mode, if it isn’t recording.
Again, this is standard on pro models, but otherwise your events will be limited to the camera’s recording time. As there are so many consumer camcorders on the market, the only way to be sure is to test out the camera, and to buy from a retailer with a good returns policy.
Next: Streaming the image