What kind of toggle switch do I need?
Your diagram shows SPDT, so that's what you need. SPST isn't going to work.

The peak current through the switch will be the same as if you connected the relay coil directly to the 12V supply without the capacitor in place. (The capacitor merely causes the current to decay down to zero from this peak value.)

Therefore, if your 12V relay has a coil resistance of 400 &Omega;, the peak current will be 12V/400&Omega; = 0.030A.

With a 220 &micro;F capacitor, the relay will activate for roughly 50-100 ms each time the toggle switch changes state. The exact value depends on the holding-current requirements of the relay.