If it was my space based on what you shared in no particular order:
- Mineral Wool Insulation in 1st floor ceiling to provide some insulation but also substantial noise deadening in support of future plans for upstairs, Rockwool Safe 'N Sound or similar
- Insulate the walls on 1st level with batt or blown in insulation or if have the money spray foam as it looks like you've got 2x6 framing so 1-2" of spray foam for air sealing then R11/R13 batt on top of that would be hard to beat
- If doing spray foam and can do it, insulate the upstairs and roof deck at same time as your cost per sq ft of insulation will be better doing it all at once vs 2 different trips months or years apart...if just doing batt or blown in everywhere the cost savings aren't as big
- Cover the ceiling, then do walls with material of your choice. If it was my place I'd put metal liner panel on the ceiling, walls would be either drywall or plywood depending on exact usage and cost of material at the time. Hanging rock on walls is much easier than ceilings for the avg garage enthusiast, but many (including myself) would just pay to have it done
- Doing ceiling first will help you keep the conditioned air where you want it and give greater thermal benefits vs covering walls(assuming walls are insulated)
- Install a mini split that is capable of 2 zones, 1 for garage and one for upstairs. You can install that 2nd zone when you're ready but planning for it now makes that future add on much easier if it's installed immediately
Another thing to consider depending on usage would be install a thermal "barrier" door on the stairwell upstairs. Especially in the winter if you're not using the upper area and doing a lot in the garage level and keeping it comfortable that heat is going to escape up the stairwell and into the un-used space. If you're not using it often even a basic sheet of foam board over the opening could make a big difference in keeping the heat where you want it. And regardless of what season it is, you need air movement for good temp control so a fan or two to keep air circulating and enable a consistent temp across the space is important.