6kW means almost invariably a 3 phase supply, so best is a 10kW motor contactor, with a 24VAC operating coil. Add a small industrial control transformer, so you can have a 24VAC rail to do the switching, along with powering the controller using some small 24VAC input power supply, either linear or switching, and use a relay to drive the contactor coil. 20A 3 phase breaker to do wiring protection for the lights, or 3 separate 20A breakers for fail safe operation ( only lose a phase on a fault), and you could add in a motor overload to detect loss of phase or short to cut the contactor coil in case of fault.
Reason for 3 phase ( 4 wire plus earth) is you can use regular 2.5mm house wiring for the cabling to the individual light standards, instead of having to use a much more expensive 6mm cable to provide the power. Lower cost ( as you will likely be using 300m of cable at least for the lights) and well worth the extra cost of the supply cable, which have 4 cores instead of 2, but the overall cost of the cable is reduced.