Anything related to math, e.g., applied maths, theoretical maths, and statistics, is in high demand in finance, let alone other sectors, especially if you've got a base degree or focus that matches, e.g., an S.B./S.M. Bioengineering/Biology or an M.D. if you want to do principled biomedical work. In fact, with the right position, you could easily spend all day publishing biostatistics papers in Biometrika, Biometrics, the Journal of the American Statistical Association, and the Journal of the Royal Statistical Society on, say, models that analyze the effects of some treatment or drug under development, yet get paid more than someone doing the same thing in academia.
Touching on your overall concerns and questions, here are a laundry list of things that I found useful during my graduate years, with respect to a career in academia:
- Take some time to really figure out what you want to study and, ultimately, do in the future while you're in graduate school. If you don't have a firm plan, it's not a bad idea to stay in graduate school longer, provided you have grant funding from your adviser or a fellowship, to pursue other options or investigate other disciplines.
- If you are committed to being a researcher, figure out why the top scientists are where they're at today and maneuver yourself accordingly. For example, within machine learning, people like Michael Jordan, David Blei, Zoubin Ghahramani, Bill Freeman, etc. are successful because they have a somewhat strong statistical background and statistics makes up a large portion of prominent pattern recognition schemes; if you were in, say, computer science or electrical engineering and wanted to be a prominent contributor to the field, it would probably be wise to pursue an S.M./Ph.D. Statistics or an S.M./Ph.D. Applied Math to ensure that your skill set is highly developed. With respect to condensed particle physics, on the theoretical side, you'd probably be well-served by pursuing an S.M. Mathematics, with a focus in differential geometry, topology, and algebra, while, on the practical side, having some programming knowledge wouldn't hurt.
- If you're wanting to do research within academia, determine, as early as possible, where you would ultimately like to obtain a faculty position. This will dictate where you should complete your terminal degree, since, once you graduate, unless you do some incredibly amazing work in your early years, happen to work with someone very famous, or are nearing retirement with a large body of work, you will mostly be constrained to moving laterally, slightly up, or down compared to your alma mater's ranking. As an example, if you want to work at Stanford, it'd likely be good to do your Ph.D. at either Stanford, UIUC, MIT, Harvard, Cornell, or UC-Berkeley.
- If you're unable to get into a really good school during your first round of graduate applications, and you know that you'd like to teach at one, either settle for a somewhat mediocre school to start out with, especially if they offer you a research assistantship, or pursue a second undergraduate degree at your alma mater. During this time, you should ascertain how the current crop of graduate students at the good schools got admitted. If it was based upon publications, find out what journals the "best" publications are in your field are being sent to and start targeting those venues, if possible, before you reapply. If it was based upon internships, try to do more of those at better institutions/labs. If it was based upon the "old boys network" and recommendations from a trusted source, surreptitiously determine, e.g., by looking at publication records, if anyone you're either working with or that knows you well happens to have either collaborated with someone at or graduated from a better university and if they can put you in touch. (I say surreptitiously because, if you chose the mediocre graduate school route, blatantly asking someone like your committee adviser about moving to better university, especially when that move is still a bit in the future, can cause them to basically yank your assistantship funding away and give it to someone who is going to stay there much longer.)
- It's a good idea to apply for as many graduate fellowships, like from the National Science Foundation, as early as possible, as you may get lucky and have four years of tuition paid for along with a generous living stipend. (Unfortunately, the NSF's process for handing out these fellowships is still a mystery to me, as they'll give one to a non-minority, male EE student at MIT with one publication at a mid-/top-tier conference and skip over the non-minority, male EE student with 20 top-tier journal publications at someplace like Texas A&M or the University of Florida.) Since you won't likely have the chance to apply for fellowships until you start graduate school, be sure and pester departmental faculty, once you're accepted, about a research assistantship. (However, don't ask them for such a position before you are accepted, though, unless you happen to be introduced to them from a known third party, as they get tons of emails from foreign nationals about such matters on a daily basis and those emails go straight into the trash can.)
- Most importantly: never piss off your adviser, as you can quickly find your education sidetracked, your reputation unduly slandered, especially if they are petty and vindictive,, and your chances of easily switching to another school dashed. I ended up inadvertently making that mistake and it derailed my Ph.D. EE and M.D. for two years, forced me to basically redo my both degrees, albeit at a much better institution, and cost a pretty penny to sue him for assault and libel before eventually settling.