hi pescody,
the question about 'available' current from a power source, driving a device that requires less current than the 'available' current is a very old one.
If the device is correctly rated say, 1amp to operate at say 120vac 50/60hZ, then you can it connect to any 120vac 50/60hZ power source, providing the power source can 'deliver' more than 1amp [as per the example]
Regarding driving incandescent lamps, remember the 'cold' resistance of
lamp will be quiet low. So the 'inrush' current during lamp wamp up time, which is usually quite short, can be 10 times the running current.
These inrush spikes can cause interference in your low level circuits, so
use good filtering.
Regards
EricG