Ditch the PicoPSU and get a real PSU like the M1-ATX or M2-ATX (fit in the VoomPC/Ampie case both versions). Then hook it up to power, ignition, and ground and voila. It is exactly as you want. The PicoPSU line is a horrible choice for the CarPC application, and last I checked it did not regulate the 12v+ line meaning when your car is on, you are sending 13.8v of dirty voltage through your brand new via motherboard when it is supposed to only have +12v stable. So bad idea.
As for the actually wiring, you need a wire stragiht from the battery (8awg or 10awg will be fine, but I suggest 4awg so you have plenty of extra room in case you decide to upgrade later). DO NOT POWER IT FROM YOUR CIGARETTE LIGHTER SOCKET. Then the igntion wire can be any source that comes on when the car comes on, usually found under the steering wheel. Then ground is your choice between the closest metal point clear of debris, or all to the same point. The grounding issue is a fierce debate about how to best prevent ground loops. You can even run it all the way back to your battery if you want. As long as the music sounds alright to you, then it doesnt matter.
As for the toggle switch, put a switch on the ignition line of your new M1/M2. You need an ON-OFF-ON toggle switch. Meaning the lever can be up, down, and in the middle. One ON pole should go to the normal ignition wire that is live only when the car is on. The second ON pole should go to a constant +12v source that is always live (can be from the radio harness as this is just a remote trigger wire and microamps are pulled from it). So if the lever is on ON #1, it will work normally and turn on and off with the car. If the lever is in the middle and connected to OFF, then the M1/M2 never gets the ignition wire on and the PC never turns on regardless of the state of the car. If the lever is on ON #2, then it will always receive the turn-on trigger and will remain on no matter what the state of the car is.
Oh, and all these questions are answered in the FAQ section too. I reccommend you check that out.