Connect 3 circuits to one switch
The simplest solution is to use a 4-pole switch.



Figure 1. An on-off-on type 4-pole switch. Source: Sparkfun Switch Basics.

You need:


3-poles (individual contacts) minimum.
1-way or single-throw where each pole is either open or closed


So at a minimum you want a 3P1T switch. A 4P1T or 4P2T (double-throw has changeover contacts).

The type in the image has a centre off position so it's probably not quite what you want.