Well, you've gone this far may as well finish it up right. This could be a great looking room given a little more effort. I can tell from the photo the way it's hung, the drywall is going to show the joints. Darker colors will show less, but the garage is going to be very dark without a ceiling. Ceilings reflect light.
If this is going to be a permanent room and you want to do a nice job, what I would do is hang drywall on the ceiling and get a pro drywall taper to come in and get it all as flat as possible. They can hide the joint irregularities pretty well with mud and are fast. A good taper eliminates a lot of sanding - it's really a skill. They have special tools that make the job a lot easier. I've taped some and got to be OK at it, but nothing at all like a pro.
Hanging drywall on the ceiling is not difficult if the joists are reasonably level to each other. You can check the joists by taking a long straight board and pressing it up against the joists all over the garage and shim any low spots. What you do is get a buddy to help and with one guy in each end, screw the drywall on just like a wall installation.
I would minimally put in a baseboard and caulk it to take away hiding spaces for spiders and minimize moisture seepage into your carpet. I prefer a light ceiling color myself to reflect light.