Looking at that video I'd say it's probably 100mA of white led or leds.
Though it's hard to tell just what might be needed if the device was outside in bright sun light.
The only way to know is to buy a few types and see how well they work.
If you don't need the full 1watt then you may find it cheaper to use 1-4 50mA high flux piranha leds rather than one 350mA 1W star led.
Just make sure you use wide angle leds. They are so much better at illuminating things evenly.
Anything over 100deg is fine.
If you're looking for places to buy lots of leds for cheap check out these two places
http://www.hebeiltd.com.cnhttp://www.besthongkong.comI've used both before without any issues.