The safest way to be sure you are studying for the right exams to get onto a particular university course is to find out directly which subjects that particular university recommends. This information is often available on their website. If not then you can contact the university admissions office. If you are thinking of applying to Cambridge or Oxford, then contact the College that you expect to apply to. The important thing is to get direct advice before you choose the subjects that you will study for A-levels, Scottish Higher, IB, or other exams.
Having said this, the main background material required for most engineering courses is mathematics and physics. If at all possible, take something equivalent to Maths + Further Maths A2 at A-level. Take Physics, and if you are interested in Chemical Engineering, take Chemistry. Beyond these, it is more difficult to give advice. If you are taking A-levels, it is generally better from a university admissions point of view to get good results (at least grade A) in Maths, Further Maths and Physics than to take more subjects.
The Millenium Mathematics Project provides excellent online resources covering more than just maths. Isaac Physics provides an exciting range of problems and exercises. The HE+ project offers a wide variety of help in developing academic skill in preparation for university entrance.