I imagine a lot of lights...with a LOT of current inrush at start-up.
A standard lighting controller could be programed for sequential operation.
I would not worry about inrush currents unless we had 100's of fixtures.
We do a lot of site lighting and switching on 100 to 200 - 1000 watt MH fixtures in one shot is common with no problems. Usually an entire panel(s) is contactor controlled.
However I do not think we are talking about a stadium here, just a house with a court.
As he mentioned the switch beside the panel why not just get SWD rated breakers?
Beyond that a simple multi-pole contactor would be a simple way to go.