choosing uni major and A level units

What unis are you planning to apply to? In the UK, you do not normally "major" or "minor" in subjects as described - you apply to a specific degree programme from the outset, which may have a structure which indicates some form of "major/minor" relationship (for example, the MSci Mathematics with Mathematical Physics at UCL, in contrast with their MSci Mathematics and Physics). If you are looking to study in another country, you may find some advice on here slightly more limited as this forum is predominantly comprised of UK students. If you specify where though, someone may have some familiarity with that country's higher education and admissions procedures.

Within the UK, the A-level Maths (and Further Maths) courses are no longer modular, and so all students study the same topics in A-level Maths, and have 50% core/shared material in FM, with options - some of which approximate old modules, and some of which don't. The Further Maths Support Group have a lot of information about the new syllabuses and options here: http://furthermaths.org.uk/2017

However under the old scheme it was very rare for specific options to be required, beyond the usual core modules that were required for all students. If you wish to tailor your programme to match the UK students syllabus as much as possible, then beyond the usual C1-4, S1 and M1 I believe approximate the new A-level closest (as they cover both stats and mechanics, although I believe it's slightly more skewed to mechanics). This would comprise the full A-level Mathemaics for the international syllabus I believe, in terms of module requirements.

On Further Maths (which you would presumably be taking to some extent to take all those additional modules listed), I think it's harder to say, since different exam boards had quite different content for the FP modules. However taking as many FP modules as possible would almost certainly cover all core FM material, and possibly some beyond that (e.g. some of the additional pure oriented options in the new FM syllabuses), but you may find FP1 and just one of FP2/3 will fit closely enough.

For Maths degrees in the UK for some of the more demanding/competitive courses (such as Oxbridge, Imperial, Warwick, UCL etc) it's sometimes recommended to take as many mechanics options as possible, as these provide better preparation for the course than the others as they often have a number of required applied mathematics/theoretical physics modules/papers. I'd note there are exceptions even in those - for example the Mathematics & Philosophy joint school at Oxford includes none of the applied maths/theoretical physics content (and is thus just all the pure maths, along with the philosophy and logic content).

I doubt it will make any difference at the admissions stage which you take, the view regarding the mechanics modules is more with respect to actually doing well on the course once you get in. Thus, beyond taking "core" content (C1-4 which are required, S1 and M1 if applying in the UK, and if applying in the UK with FM probably FP1 and either FP2 or FP3 - you'll have to see which fit the syllabus best from your exam board), it's really up to which you think you'll enjoy the most and (partly as a consequence of this) do the best in.

Regarding employability, there are a lot of things that could be said, but any numerate degree is eminently employable, and focusing on pure mathematics allows you to much more strongly demonstrate your ability to think and work abstractly, which can be a strong selling point if you present it right. Ultimately a lot of employability comes down to the transferable skills learned in the degree, and how well you present and leverage those to your advantage. Outside of e.g. continuing in academia to specific PhD projects (and you can probably quite easily go from undergraduate "pure" maths to an applied/theoretical physics or stats/probability PhD project, although it might slightly depend on your options taken), the actual content of your degree is largely less relevant.

For the roles where it would be (e.g. some engineering roles) you would normally need a degree in that specifically anyway. In terms of computing and software development, in the UK at least there are many such development roles available to students of a numerate degree (and not infrequently, any degree) where they will teach you all the necessary programming and development skills in the course of the job. So you shouldn't concern yourself so much with that aspect until you are actually on the degree.

thanks for all that....I heard Princeton is a good university for math and physics. what do you suggest I should do in order to get there? thanks for your time again

thanks for all that....I heard Princeton is a good university for math and physics. what do you suggest I should do in order to get there? thanks for your time again