I suggest you start by deciding what sort of water pressure and maximum volume flow rate you need, then spec the water supply for that. If at all possible I would use low voltage DC for everything because mains voltage electricity plus water spraying about is a recipe for disaster. What ever else you do, if this thing is powered from the mains in any way make sure you power it through a residual current detector (RCD) isolator.
Assuming you want to allow multiple 'guns' to be used in the same game, I'd eliminate the solenoids and just give the user a hand trigger, the sort of thing commonly seen on garden hoses - and if it suits your game design, I'd aim to use standard garden hose spray heads with a suitable nozzle. That way you can turn on all the guns together by turning the pump on, or opening the valve to your pressure accumulator. I don't know how much water you plan to dispense per game, but an ordinary garden pressure spray container would make a convenient pressure accumulator.
The electrical and software side should be fairly simple, but you can't finalise it until you have sorted out the hardware side and decided what sort of pumps and valve actuators you need.
To detect water hitting the target, you could just use a paddle that operates a microswitch when a water jet impacts it.
To detect the water level in your measuring device, I would use a switch activated by a float. Make the float something visible and you can use that to show the progress of each player during the game.