It depends on how much ventilation you've got in your attic.
This article provides the most useful and thorough information source that I've managed to find.
For what it's worth, my attic above the garage has the blown in insulation resting on the sheetrock, but then again, I live in Alabama.
I have a few questions and observations that will effect what you should do. First, I see that the peak (ridge) seems to be over the existing framed and drywalled wall. What is on the other side of this wall? Is this garage attached to the house or free standing? Do you have or intend to put any heat or heat dump register in this space?
I also noticed that the roof framing is standard trusses, not attic trusses. Where is the attic space going to be located? If the attic space is going to be over the bay you pictured, then you are limited in the amount of insulation you can install and still have a floor for storage. If the collar ties are 2X6, then the most blanket type insulation you can install is R19. 2X4= R11. Fiberglass blanket would definitely be the most cost effective in a small space such as you have. I would use unfaced F/G, and a 4 or 6 mil plastic vapor barrier installed before you drywall. As for installing drywall, you really should install strapping at a max of 16" on center to mount your 5/8" fire rated rock to. 24" inch on center is too large for hanging rock overhead, especially 5/8" rock. If garage is attached, 5/8" drywall is minimum code in most areas.
I also noticed that you have a metal roof. Metal roofs are great, but are notorious for condensation. This makes it absolutely necessary to have a good vapor barrier and good venting to avoid potential interior "rain storms" lol.
My other consideration would be insulating the exterior walls. Since there seems to be only one long wall and very little framed cavity wall on the gable ends, it would be advantageous to go ahead and finish the job by insulating and drywalling these walls. If you only do the ceiling, you will not have a good barrier to air, heat and humidity leaking by the ends of the ceiling at the wall plates and entering the attic area. This kinda defeats the whole idea of what you are doing.
Best Answer
If you run the engines of the cars in your garage then that is probably source of the high humidity and the moisture. If this is the case, then you need to vent that area when the engines are running and for a short time after the engines are shut off. Burning fuels create a lot of water vapor. If it is not from the cars engines, Then i would check for water infiltration from the roof area. With all that insulation and the vapor barrier you have created a tight atmosphere in the garage. Any operation in the garage that gives off moisture will allow that moisture to collect on the ceiling and walls which can allow for mold to grow.