BB IB internship vs. F500 or CO internship

I am currently a rising sophomore at a non-target state school. As a freshman, I got admitted to our university's investment society and investment banking society because I thought that was the career path I wanted. After learning about the intricacies of IB and the exit opps vs MC I decided I wanted to change to MC. My main goal after college and my early career is a T-10 MBA and then eventually either working at startups or C-suite at a company I respect. I think MC would prepare me better for these ends than IB. My question is whether I should try to get an IB internship junior year summer at a BB in NYC and use that to prove myself to MBB or go the more traditional consulting/F500 internship route the next two years? Although I go to a non-target, we have an established alumni pipeline to most BB firms on wall street. We don't have the same network at MBB. So should I go for the BB IB internship and use the prestige to sell myself to MBB, or should I go the more traditional route? Also, if you have any more opinions about my career choices in the short term for where I want to end up let me know. Thanks all.