I've moved overseas a few times, both as a student, and then as an employee being transferred overseas.
I've typically taken two checked suitcases, fairly well stuffed, and a carry on. I'd think about what you'll need in your first 72-hours or so and make sure to include those things in your carry-on. That might include clothes for your first 2-3 days, medicines, medical records, valuables, etc.
Are you shipping other belongings or are the suitcases it? If you're shipping stuff and going to a furnished apartment, then two suitcases could likely be plenty to tide you over.
If you're not shipping other things, you may want to take an extra suitcase or make arrangements to ship some belongings. Moving companies should be able to ship those for you at a much more reasonable cost than mailing them. It may take several weeks for your shipment to reach you, but you'd have what's in your suitcases to tide you over.
Everyone's a little different as to what they need when they move overseas. Some people are happy with just what they can bring in their suitcases and will be willing to live simply and/or buy what they need once they get there, others prefer more touches of home or don't want to shell out to buy things they already have at home. It may also depend on how long you intend to live there (is it a temporary appointment or will you be living there indefinitely, for example.). If it's just for a year, you might not want to ship a ton of stuff from home, but if it's indefinitely, you might want to ship things rather than re-buying.
And, as others have said, it may depend on your situation when you arrive. If you're going to have to take a train/bus to your destination, then less luggage (and maybe shipping stuff if there's still stuff you want to bring from home) is probably better, but if you're flying in to your destination city or have someone picking you up, then you can handle more luggage. There will almost certainly be taxis that can handle several pieces of luggage or large or odd shaped pieces at the airport if you're flying in to your final destination.