For example what is doing the triggering?
A mechanical trigger switch, which is the essential part of the question.
As for the capacitors I'm not sure what your intentions are.
To discharge and activate one of the solenoids when the switch pushed to off position, for example.
The simplistic circuit could look like on the picture. It has a few flaws that I would like to avoid. First, it need DC, so I need to rectify 16VAC I have. Second, if the switch is in 'on' position during power up, the top solenoid will be activated right away, and I would like that to happen only when the trigger flipped one way or another.