Honestly, you are better served by working a few years before going back to school.
An MBA is pretty much useless and a waste of time and money without work experience, because the kinds of jobs you'll get coming out of it won't be much different than what you'll be going after right now: entry level jobs for college graduates.
Masters in Finance programs can be a possibility without work experience, but if you're going to do that, focus on North American programs. Unless you have citizenship in an EU country, you'll have a tougher time looking for work coming out of a EU school without any work experience -- and you won't be any better off than you are now by coming back to North America with an EU masters degree and no work experience.
Again focus on getting a full-time job after college. As for what kind of job, that is entirely up to you. B-schools get folks from all walks of life: bankers, consultants, engineers, accountants, marketing professionals, product managers, military officers, lawyers, doctors, etc. It runs the gamut.
Don't focus on what kinds of experience stands out (because you'll be choosing a full-time job based on what others perceive). Focus on what you want to do.
Follow me on Facebook