It largely depends on the companies you are shooting for - how many MBA spots they have and how many people are gunning for them. In my experience, grades in bschool don't matter when it comes to finding a job. The same goes for extracurriculars. I've seen a lot of people with excellent grades and lots of xc involvement fail to get a job on campus whereas people with less than stellar marks, but really focused on recruiting and networking had several offers.
The firms care about several things: do you have basic knowledge about the function you are recruiting for; do you really want to work in the industry or you have just dropped your resume as you did with 30 other companies; do you fit with the culture of the firm. That's why you need to demostrate BASIC knowledge of the principles of marketing, finance, or whatever function you are recruiting along with knowledge of the industry and the company, which shows that you are interested enough to learn about them and think through the issues facing them. The fit portion is hard to be faked - it's just about the way you are used to doing things and how you think.
Excluding IB and consulting, about 30-35% of the traditional industry jobs are open to internationals. The main problem that most internationals had in securing jobs was communication skills. I saw many people with less than stellar English skills and they didn't fare well in recruiting. If your English is less than fluent, I would recommend improving it as it would really put you at a disadvantage - you are competing with native speakers, so your ability needs to be pretty close to theirs. That is even more true for MC and IB. I saw people jump on the IB/MC bandwagon without considering whether they would be a good fit for the job only to get dinged in their interviews - by that time interviews for other industries had started and these guys were left with nothing because they hadn't networked with other firms.
So you need to really decide what kind of job you'll be after before arriving as the recruiting process starts pretty soon after school starts. It's hard to generalize for all possible jobs, but one recurring theme I noticed was that showing interest and networking with people from the company is much more important than having good grades in marketing or finance that no one looks at. Even previous experience in the function/industry will not get you in if you cannot show interest or if you don't click with the people from the company and have bad communication skills.