...it seems there's a lot of push toward CS/DS in the comments.
They are the current "hot areas" in all fairness and, while markets can change rapidly and all that, CS in particular probably won't fall in demand.
But those generalisms shouldn't be your concern. You get good at a niche, which is what your math/physics training affords you to do, so that if blah falls in demand you're not screwed. I definitely see that where some of the web and data projects I do for clients use technologies not in demand, but where the specific niche work I do is in demand. And I saw it before in finance where my specific credit skills were sought after during the recession, but where people with more general skills suffered because of general market conditions.
In terms of the "multiple choice", my view is that it's no harm in undergrad to pick wide areas, but that you should narrow down as you go on through MSc/PhD and into work. As soon as you enter a career you will probably have to specialise, although it's not impossible to generalise a bit.
Also don't forget to also develop other skills - having a good contacts network, communication skills and business acumen for a start. Thing about corporate world is it's not enough to have these skills, you have to be perceived to have these skills and make it obvious.
Otherwise you will wind up being pigeonholed as "good with numbers/technical/quant stuff but nothing else" - I worked with someone in finance who's previous career as an engineer plateaued because he was perceived to be just good at technical work, nothing else. Thing is when I worked with him he was practically a guru on client relations, marketing, soft skills etc. I'm not sure if management's naive prejudices about math/physics/engineering graduates came into play, but his mistake as an egineer was defintely that he didn't make it obvious he had these soft skills. People often mistakenly call this "hiding skills under a bushel" - I feel it's more that he didn't have the savvy to realise he had to be so upfront about it. A lot of people in their first career treat it like a "job for life" and switch off and expect opportunities to come to them rather than create them tbh.
