14-3 is probably 14-3 w/grd, and you only need 14-2 w/grd.
14-3 w/grd has a white, a red, and a black wire, plus a bare wire for ground.
With incandescent bulbs all you need to do is take the wattage and divide by the voltage (120) to get the amps. Thus each 100 watt bulb draws .83 amps. Lighting loads are continuous and as such you cannot exceed 80% of the circuit rating. So on a 14 gauge wire/15 amp circuit, you are limited to 12 amps........ and on a 12 gauge/20 amp circuit, you are limited to 16 amps.
Not sure why you want to use 100 watt bulbs, thats a lot of current burning up. I'd consider compact fluorescent bulbs (CFL) instead.
Charles