So I’ve been asking some advice and most of the people I know have told me that if I had a question, I should ask the TA instead of the professor and that some professors (I go to a pretty big school) don’t want to be bothered by their students. However if I want to do research or really take an advantage of the fact that many of my professors are top notch and get a deeper study, what should I do? When would be visiting OH be appropriate?
Most professors love to talk to the students, particularly if it is more in depth about some aspect of the coursework. If you need to find when the final is or where the discussion section meets, you should probably ask the TA.
Of course, it’s appropriate to visit during office hours. If there are multiple students there, professors will probably prioritize students who need help with the course, over those who just want to chat. But I’ve never known a professor who wasn’t willing to talk to their students, even if it wasn’t directly related to the course. Often, students who went off on tangents in class were redirected to visit the professor during office hours to discuss it further before they took up too much class time. You could also make an appointment to meet with a professor outside of class and office hours as well to talk. My school had a program where you could get coffee or lunch with a professor paid for by the school to encourage students and professors to talk outside of class/office hours. And there’s nothing professors like talking about more than their research.
i would approach them about research like after one month…but during that one month, approach him a lot and ask questions…
or sometimes just email profs for research positions or shadowing…most of them really want students!! you’d be surprised by their responses 
Visiting office hours is always appropriate. Professors I have known love to students stop by. Granted, I go to a smaller, medium sized school, but I think the same concept applies elsewhere. That is what office hours are used for and I think they aren’t utilized as much as people think. See if there is a time you can drop by, preferably when no one else is there to chat about that or seek him out in an appointment after class. It build great repertoire and shows that you are interested in the class outside of just the class material. I went to my environmental science professor last semester and he says he loves to talk to students about what he does because most of the time when students visit him it is about “bumping up their grade” which annoys him.