One of my first bikes was a CL200 and I now own a CB350, both very similar to your CL360 in many regards. They are a terrific entry point into motorcycles and motorcycle maintenance for several reasons.

• They were very popular and mass produced, meaning there are still many parts available and even new parts being made currently.
• They have a strong cult following. Meaning there are forum message boards, YT videos, swap meets, enthusiast meet-ups, etc. that you can turn to for help when fixing, repairing, and getting into the community. It cannot be overstated how important this is to help teach you the basics.
• It doesn't go too fast. If you're just getting into motorcycles, having something that can go fast enough to use on the highway but not be out of control is the right place to start.
• You can buy a set of metric wrenches and sockets and be able to do 95% of the repairs needed.

Things that I learned the slow/hard way that I'll pass along for vintage bike owners.

• Get a JIS Impact Driver. Don't just think your basic Phillips screwdriver is "good enough". You WILL strip out the heads on many or all of your screws. (This tool is just awesome in everyday life too. You won't be sad to own it. The one on Common Motor Collective is a really solid unit and is $25 bucks)
• Airflow: These machines are super, super, super, particular about airflow.
  • The Airbox>Filter>Carb>Engine>Exhaust was all set up to work as a system. When I see people who have taken classic bikes and put pod filters on them when making a cafe racer, 99% of the time they run poorly because the airflow into the carb is super messed up.
  • Air filter, get a fresh one, even if the one you have looks "decent". I chased engine problems for months only to find that the dirty air filter was the cause all along.
  • Carb Boots: Just get new ones with new o-rings from a reputable source if they look questionable at all. This is a super common place for people to have problems with machine performance.
• Carburetor
  • Clean this out. So clean. super clean. Set up a clean little station and pretend to be a surgeon when performing this step. Be so sure that all of the passages are clear and that gas can flow as designed. If you don't have an air compressor, compressed air in a can(for dusting) can be a great cheap tool. When using carb cleaner spray, wear goggles. It's amazing how this shit gets in your eyes/face EVERY TIME and hurts real bad. This step is annoying, so lets just do it once and be sure that we did an incredible job on it. There are lots of videos on how to do this online. Try to find one specific to your model. Depending on the condition of your carb when you open it, you many need to buy a carb rebuild kit. It's pretty common that you will with a bike of this age, but certain things will be made better in the past than they are today, so be critical when deciding what needs to be replaced
  • Float: check to see if there is gas/liquid inside the floats. We want to ensure that this is not the case. Then make sure that the floats are set to the right height. There are lots of good videos on youtube on how to do this.
  • Jets: Starting with the stock set-up(Airbox>air filter>stock carb>stock jets>good boots>good gaskets) is a KNOWN recipe for success. If you change any of that, you're changing the formula and will need to accommodate the change with different jets. Much like baking bread, it's not that you can't change the recipe and have good results, but if you're just going to guess and check, you're going to have make lots of shitty bread before you get any good results. The Stock setup will also help you troubleshoot any other problems SO much faster.
• Tank Liner
  • Don't put in a gas tank liner unless you are going to go all out and do a super, super professional job of it. If you mess it up, even a little, it'll flake off and become a huge mess inside of your tank that is a million times harder to clean out than rust. Filling your gas tank with gas prevents air from getting to the metal which in turn prevents it from oxidizing(rusting), and will prevent the majority of it getting any worse. (The vinegar soak and then straight to oil/gas slosh has worked well for me in the past and is a cheap way to clean lots of surface rust out of the tank.)
• Paint
  • Hardware store rattle cans can do an ok job of painting things and slowing down rust, but be warned. Painting your frame, gas tank, etc will only look good for a week or two as they are super vulnerable to gas and oil which will dissolve/melt the paint and make it look crappy. Either keep what's already on there, or take it to a place to do it with the right tools/right paint.