Best Path for PhD in Engineering - which Undergrad Major at which Colleges?

Keep in mind that faculty members at many schools (particularly at “top” schools") are averse to admitting applicants from their own undergraduate departments into their university’s graduate engineering program. They prefer to diversify the gene pool, so to speak. Students who get their science or engineering MS or PhD from their undergraduate alma mater are relatively uncommon. Not unheard of but uncommon.