What are some tips when it comes to taking care of your car?

I own a 95 Honda Civic EX and it's been well taken care of by the previous owner. It has only 47k miles on it because the owner would only drive around for small tasks. I know I should check the fluids such as coolant, oil, windshield wiper, and brake fluid as well as replace the air filter and oil. I also rotate my tires and check for tire pressure every now and then.

I want to know what else I can do in order to maintain this car in top shape so I don't run into any trouble.

Added (1). Also, I know that it is dirty under the hood of my car. Could I go to some car wash where they clean it or would it be better to do it myself?

Did the car come with its owners manual? If so, there will be a section explaining what maintenance is required at various mileage levels. One of the more critical ones for Honda vehicles is replacing the timing belt at, I believe, 60K miles for older models. If it breaks, it can destroy your engine.

Be VERY careful washing your engine. You can get water into the wrong places and cause problems.

If you check the questions on here you will see at least once a week people wondering why their car won't start after washing the engine bay. Don't do that. The underhood area is designed to keep water out for a reason.
Older Hondas need their valves adjusted on occasion. Not expensive. A tune-up would be good at this juncture also. Watch for trailing arm bushing wear. If an alignment is ever needed get the 4 wheel as this car has rear adjustments. A fuel injector cleaner in the fuel tank would help too.