I’m a Purdue MET (mechanical engineering technology) grad. So I’m biased but engineering is for sure the way to go in your shoes. Once I learned about the school of technology it made for a perfect fit, it is more hands on and less theoretical i.e. you will have lab classes where you run a lath, mill, and weld also pour castings. Helps to make you very well rounded, Purdue West Lafayette also has several student groups that are involved with some type of motorsports. I know the IUPUI motorsports deal has very similar class to that of MET.
At my current company we are looking to hire an engineer …. It will be a Purdue MET grad if I have any say.