Lucrative and respected STEM fields in Japan

I will start off with a brief bit of anonymous information about myself in relation to this question:

I received my A Level results last August (2016): A* in physics, A* in mathematics; A* in further mathematics and A in chemistry.

Currently, I am looking into applying to a Russell Group university, probably Oxbridge (Cambridge or Oxford), for an undergraduate STEM degree in either physics, mathematics; engineering or computer science.

In secondary school I was lazy and complacent and therefore only attained mediocre GCSEs as a result of this, however, I am confident that my A Levels should provide incentive for either university to accept my application.

From my early teens I was very interested in Japanese culture and history; the traditional rather than the modern. Though, I find the technological and scientific proficiency of Japan as a major draw to visit and hopefully expatriate at some point in the not-so-distant future.

I am currently learning keigo Japanese as a proviso for visiting and possibly creating a life for myself there. I am also looking into learning less formal Japanese as to be able to communicate on a daily basis without sounding like an idiot.

So, this brings us to my question:

What STEM fields in Japan are considered the most respected and well paid by native Japanese people?

Do note, if the information given is concise enough, this will influence the undergraduate and graduate degree I shall proceed to pursue.

Japan for the most part doesn't care what your job is, it cares about which company you work at.

I care what the prospective field is, more than the prospective company as the prospective field would be what defines my pay cheque?

Among the different fields you mentioned, computer science or engineering sound more like "practical" fields of study, while physics or mathematics sound more like headed for researcher type of careers - what do you want to do as a career for yourself? That's what you should be considering.

Also your language proficiency might become an issue in some fields - maybe not much of an issue in computer science (if you go into software/app development and similar jobs), but other jobs, where you need to interact with colleagues or clients on a daily basis, would require good proficiency in the local language, both speaking and reading/writing.

About language study, you might be starting off on "polite" speech, if that is what you mean, but you will need to learn the whole grammar including the "informal" speech as well (for conjugations and expressions requiring verbs conjugated based off from the "dictionary" form of verbs, for example) to be able to communicate properly. And this will take quite intensive study over an extended period of time.

More than "what STEM fields are respected by native Japanese people," you should be asking "what STEM fields are companies in Japan looking to hire workers from overseas for." Practical skills like engineering and computer science are still sought after, and I know several very well paid American and European programmers in Tokyo. If I were in your position I would be studying programming languages as well as Japanese.