"I'm about to graduate with a skillset that points to a bunch of different jobs (applied math, finance, business.) How broad or narrow should I make the scope of my search? Learn as much as possible about one job title, or get different resumes and try various options?"
This is a good problem to have - you sound smart.
Since you have options, one idea is to focus on which individual company you want to work for. Do some research on companies in your area that have jobs that relate to your expertise. Then, do more research on which of these companies seem to be the best to work for and receive recognition for doing so. Great benefits, work culture, leadership, growth opportunity, etc.
Finding a job in a company that will allow you to thrive and support your growth will give you a strong foundation for your entire career.