Choosing an undergraduate research advisor
Talking to some other students who went through this before me, I have heard that one should take a class with the professor before asking them to be one's research advisor (I thought this was BS and tried reaching out to profs, but got stonewalled - this seems to be systemic in my uni/dept).

Well, take it from a professor's point of view. They received an email from a student they don't know, who's only vaguely interested in their work. If you don't even know what subfield you're interested in, it's hard to write a convincing email explaining why you're interested in their work.
Mentoring an undergraduate is a time investment, not a time saver. So professors like to see motivated students who understand the problems they work on in their lab, which is part of the answer to your question below.

Why is it better to find a new prof rather than using a well-known prof?

Some people might say that older professors are busy as heck, and a newer professor might have more time to invest in a promising undergrad. Unfortunately, with COVID, finding a professor with time for an undergrad will be harder.
However, this isn't universal, and you should talk to previous students before assuming a professor is a good or bad mentor.
In summary, identify a few top professors, take their classes (as was suggested), and do well. That's at least a foot in the door to open the conversation.