I am currently four years into a chemical engineering degree, and i think that if i was in your position, i would go with maths (the highest level you can handle), chemistry and physics. I have found that a lot of other students (especially those who did not have a particularly strong background in maths to begin with) have struggled through some of the more mathematically intense subjects (such as computer analysis and modelling, heat and mass transfer, process dynamics etc.) because they could not keep up with the maths. As part of my degree we did have to take classes in linear algebra, multivariate calculus, differential equations etc., however these were often taught at a fast pace, so any earlier mathematical preparation was very handy. I did quite well in my high school math classes, and although the math i have learned in university is much more advanced, my study of high school math gave me a very solid foundation from which to expand, and it also helped me figure out what works for me when studying math.
Although my engineering course hasn't required me to take many chemistry or physics classes, getting an introduction at the high school level did definitely help. I did have to take introductory chemistry classes at university, however, like the math, they were quite fast paced compared to high school, so I'm not sure if i could have learned as much without any prior knowledge. Honestly though, i think the biggest advantage from studying chemistry and physics in high school is the way that (especially physics) they make you think analytically, which is exactly how you will need to be thinking for many engineering classes. Maybe somebody with more knowledge can comment, but i am not sure if biology will get you thinking in the same way, especially if it is just about rote memorization like i so often hear (although in saying that, being able to memorize things well is a very useful skill).
I didn't ever study much biology, but it does have its applications in chemical engineering. I know some courses do require that chem. eng. students take biology classes (mine doesn't), but I'm not sure if studying it in high school will be as beneficial as studying physics and chemistry. As for technology and design, i am not entirely sure what these involve, however you will learn a lot about engineering technology and their design while at uni, and even more so when you start working as an engineer.
All in all though, if i had to make one single recommendation based on my experience, it would be to learn (and properly understand!) as much math as you can, and learn how to learn math efficiently.
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