Arduino project, powered by car electric system
First, a note - there is already a negative in the cigarette lighter, no need to run a wire to chassis.

For your skill level, what you are proposing is quite complex. Instead I suggest the following setup:


Purchase a Seeeduino Stalker Waterproof Solar Kit. This kit is great. It comes with an Arduino with clock, SD card and XBee interface. It also comes with a solar panel, lithium battery and the charging circuitry on board. It can charge via the USB port or the solar panel. For the GPS, you may also want to look at their GPSBee which can slot into the board.
Purchase a cigarette lighter to USB charger. This will convert the car 12V to USB 5V which can power the battery.
In the car, connect the Stalker to the USB charger, and locate the stalker somewhere on the dash or parcel tray where it can also charge from the solar panel when the car is off.
Now you just have to spend hundreds of hours writing the code and debugging. Good luck!