Monorail is (usually) quicker.
But, if this is your first time to Disney World, I would take the ferry boat (and get to the parking lot a bit earlier to compensate). I would also go up to the top deck, and stand in the front of the boat. The views approaching MK this way are breathtaking. I'll skip describing it so as not to spoil it for you.
The monorail views just aren't nearly as much fun.
Returning to your car, if you would like to travel through the Contemporary Resort on the monorail, take the resort monorail (not the express), and TTC will be the 2nd stop (with Contemporary being the first). The express monorail travels in the opposite direction, so you would get to the TTC before going through the contemporary.