I have a masters in mechanical engineering, so I would like to think I can help you out. But one question, what the fuck is stationary engineering?
edit: So, a quick search of the all knowing goggle tell me has something to do with boiler maintenance, or something like that. That being said, it sounds like you would probably need a lot of the same things I did. The school has changed the curriculum some since I was there, but it's still basically the same overall. My first year, I took mostly the basics. Physics, Chemistry, shit tons of Calculus, and my gen ed reqs. 2nd year, I took most of my structural courses. Statics, dynamics, deformables, material science..., as well as some programming. 3rd year was mostly dedicated to fluids and thermodynamics, but I also took 3 design courses. 4th year was my final project, plus some grad classes to help me get into grad school. I took a finite element theory course, a nuclear power course, and another math course to fill out my minor.
So, in high school, I'd stick to any math you can get your hands on and the physical sciences (AP classes if you can. I got a math and two Bio credits from mine). Also, if you have any engineering or CAD courses available to you, I'd take them as well.