Zurich IB Job

Hello!

I'm new in the forum and I've been getting really interested in Investment banking.
I am currently ending the senior year, about to get into an Economics or Math degree, not really sure which. I'll probably choose in August.

Well, my question is:
What should I try to do to land a job in Zurich? I'd like (obviously) to get a job at a big bank, like GS or JPM and I want Zurich since the salary is pretty high. I know the cost of living is high, but I come from a very frugal family and I intend to keep it that way. Being frugal in Zurich will make me much richer than being frugal in London, from what I've seen here about salaries.

I know I gotta start ASAP, but what should I do? Send emails? LinkedIn? I'm from Portugal, by the way. A vacation as a summer intern after my first year of college would be financially possible since its rather close.

Thanks for the advice :D