Education Direction For Undergrad Interested in Quant

Hello All, I'm an undergrad, about to be a junior, majoring in math and minoring in applied math. I've heard the job of a quant is essentially sitting around solving hard problems, which sounds pretty interesting compared to other jobs I've heard about (also the pay lol). I think I should be figuring out what I'm going to do after graduation soon, so I was wondering if I was a viable candidate for a quant and what I could do to prepare for the role? I've read multiple forum posts about this but found a lot of contradictory advice.

I've taken the standard math classes (multi, linal, analysis, algebra) and a couple of grad classes (topology, PDE, Optimization). I also know how to code in c++ and python. From here, what could I do to prepare myself for the role? Should I be taking some economics, stats, or other classes (do classes even matter for quants)? Should I get my master's/PhD degree in math (not sure a master's is financially in my cards)? Or should I branch out to another area like CS or Stats for further education? Should I be looking for internships in finance at this point (my lack of economics classes makes me think this isn't really an option)? The only activity I've really participated in is research with a professor at my school (I took the Putnam for fun my freshman year but only got full points for one question, I've never been a competition math person). I apologize if these are repeat questions.

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