Drywall – Best way to hold interior wall insulation in place prior to drywalling

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.

First off, a reality check; not trying to discourage you, just trying to set some expectations here:

• First off, the actual pressures you're dealing with are very small. Absolute pressure is measured in Pascals; 1Pa = .0001psi. Your 80dB sound is inducing pressure changes of approximately .2Pa = .00002psi (that's two hundred-thousandths of a psi).
• Second, the percentage changes you need to make to these small pressures are very large. The Bel scale is logarithmic, based on a "reference" pressure. One Bel - 10dB - represents a tenfold increase in pressure. So, a 90% reduction in the pressure of your 80dB sound only reduces it to 70dB; to get the sound level below 10dB (you or I would call that "silence"; in laboratory conditions the threshold for human hearing is 0dB) would require reducing the pressure differential by 99.99999%.
• This level of isolation is possible but extremely cost-prohibitive in most applications; million-dollar recording/mixing studio spaces are built with lower levels of soundproofing than this. You normally see this level of isolation in medical and sound engineering research labs, where they literally build a room within a room, suspended on vibration-dampening struts, with a near-vacuum maintained between outer and inner walls of the chamber.

The upshot of all of this is that, no, a reduction in sound of 80dB is just not possible on a $1000 budget.

Now, all that said, don't lose heart. First, you seem to have much more ability to make changes to your rented space than the average apartment dweller would have (though I'd double-check your rental agreement; if you're required to return the space to its original condition - or pay damages - when you leave, think carefully about studding in a new wall).

Second, much smaller reductions in SPL can make a very big difference. Soundproofing that reduces an outside noise by 20dB makes the noise sound only a fourth as loud. This is easily doable in your budget (add some sound-insulating material such as mass-loaded vinyl between the existing wall and an extra sheet of drywall or wall covering), add a sound-insulating curtain or three, etc and you'll start hearing results pretty quickly. Two layers of mass-loaded vinyl will reduce most sounds above 125Hz by 18dB just by itself.