Startup vs Investment Bank for Management Consulting

I'm currently a freshman reading economics at a tier-1 university and have spent time at a think tank, vc, and multiple startups.

My plan is to work in consulting upon graduation from college.

With my current background, should I look at joining another venture builder in a strategy and business intelligence role, a really really cool medtech startup in a strategy role (raised nearly 70M and is on track to disrupt an entire industry -- has peer reviewed clinical data) or a boutique investment bank (fewer than 40 employees, middle market, recently acquired by a large investment bank), to better develop my profile for consulting?

I've been told by a couple of people that working in an IB would serve me better, as it is 'more prestigious'. However, I'm slightly concerned about the idea that it could 'dilute' my CV - I would appear to be jumping between industries / not sufficiently focused.

I'd be extremely thankful if anyone could provide any insights.

P.S. my real passion probably lies in tech / startups - but there's no way I can join one right after college due to the crushing amounts of student loans that I currently have (I've done the math - I cannot afford to join a tech firm / startup in a non-engineering role). My plan is to work in trading / IB / consulting (preferably consulting) upon graduation, pay off my student loans within 4 years, and make the jump back to the valley.