How much does the school you attended matter?

Hey engineers, I'm changing my career path and am looking into going back to school to get a second Bachelors in EE and hopefully follow that up with a MSEE. Obviously going to a top 10 school can give you a big leg up, but when it comes second and third tier schools, how much does it matter?

I'm interested in the general answer, but also specifics to my own situation in which the schools being compared are Virginia Tech (#13), Miami (#98), and Florida International (#156) [source].

Thanks!