Welcome to the fun and sometimes insanity.
If the roof structure is exposed, you have a few options.
On my garage, the roof is made of trusses. I installed rock wool insulation (won't mold or harbor rodents and is fire resistant) between each truss. You'll need to measure the distance between each one and buy insulation the matching width. For depth, the deeper the better the insulation value. You will want to ensure that an air space is left for the soffits to allow air flow, i.e. don't tuck the insulation right to the roof line where the walls come up. Since you are closing in the garage ceiling by adding the insulation, you will also want to review the situation with roof ventilation. If there are no roof vents, you will want to add one/some. It is important for an insulated space to "breath." With rock wool or fiberglass insulation, you will want to install a vapor barrier beneath the insulation. Where vapor barrier sheets overlap, tape the joints to ensure an air tight seal. In my area, the correct tape is usually sold as Tuck Tape (not Duck or Duct Tape). The next step is to install the ceiling.
Spray foam is another option. It is usually more expensive to have done. There are kits for DIY. The techniques for spraying are different to batt insulation since you need a backer to spray against. In some applications, this may be directly to the underside of the roof sheathing. Spray foam is insulation and vapor barrier in one. The same principle for efficiency applies to spray foam, the thicker the higher the insulation value, usually expressed as the R value.
