What thickness drywall do I need for 24" OC wall studs in a detached garage?
You actually have a couple of options in this case.  The easiest option would be to simply use 12 ft sheets of 5/8 fire rated sheetrock and rent a lift to do the ceiling with.  A lift is very easy to use and almost makes it a one person job.  Personnally, I'd also use 5/8 on the walls as well. As BMitch already mentioned, mount the wall sheets horizonally and stagger the vertical joints.  You can use 2X4 nailers, (fire breaks) at the 4ft OC point, but not really necessary.  You will not see any bowing or cupping with 5/8" at 24" OC on walls.

The second, and BEST option would be to install 3/4" strapping 12" OC across the field of the ceiling, and around the parameter.  This will give you a lot more surface area to screw the drywall to and make aligning joints a lot easier, especially if the 24" joists are not perfectly spaced or square. Putting up strapping is quick and easy if you have a nail gun. Use 4D ring nails. Ring nails will hold tight and not loosen over time.

Hint: Use a chalk line on rock to mark backer locations before you hang it, or you can also mark the location of your joists or strapping on the wall before you lift the rock into place. Secure the rock with a few screws to hold it in place, then  use the marks to snap a quick chalk line marking the location of your strapping. This will assure you hit a solid spot with every screw. Ceiling screws should be no more than 16 inches apart.