Let me ask you a fun question, if you had to make a list based on what you've played and what you seen, what would be your top 3 pins that you would consider owning? Vic_Camp brings up a good point in his question. Based on your interest, the type of repair would differ slightly based on the age of the machine. Your response could also get you some good advice from the crew here on pinside.

One thing that can give you a little bit of Peace of Mind, is something that you mentioned already. You have a local arcade that you have been playing pinball machines at. That means there will be someone that is there that is able to repair machines. In the short-term, you may be able to engage some of those individuals to help you with your machine in case you run across any issues. 27dnast has a great suggestion, and I think everyone would agree. First thing you need to do is find a machine that's working really well from the start. That way, you can play around with things that are very doable, like replace burnt out lights, change out incandescent bulbs for LEDs, if that is your preference, Etc. That will get you comfortable opening up the back box, taking the glass off and liftingvup the Playfield, the basic moves to access the machine in itself. You will be surprised how quickly you start to feel comfortable with basic access moves to the machine.
But all that said, if you have a machine that is known to be in good working order from the start, it'll be a little while before you need to do anything. You will find yourself doing the above just out of pure interest and curiosity. The more you read, the more modifications that you see people doing, the more encouraged you will be to do some of that stuff yourself.

Keep us posted, welcome to an awesome hobby, and let's hear what those top three are!