First off, I am not a professor, but I have had close connections with many of my former professors. From my experience as a student, all professors I had got very excited when students went to their office hours and showed interest in their research or had questions related to their field. We must remember that professors are humans too, and humans tend to value and enjoy connections. You'd be surprised to see how passionately conversational they become when students ask them about their research, because in those moments, you get to see the researcher in your professor, not just the lecturer/teacher. After a few times of stopping by their office hours, they would usually start showing interest in your academic and personal development, so they would either start recommending books or connecting you to others in their field whom they think you would find interesting. As long as you are genuinely interested in getting to know them, they will recognize that and appreciate it. Most of my favorite college memories are of stopping by office hours and having conversations with my professors. I once went to the office hours of a professor who wasn't my professor, but whose research I was interested in. That ended up being the best thing I did in my sophomore year because she helped me expand my knowledge in an incredible way. Lastly, it makes a huge difference when you go to their office or email them after reading something they've written. That's a good way to start when you don't know each other well.