Bare minimum, with which you can do just about everything:
a 10" French knife (or 8" if you are very small)
a paring knife
a flexible boning knife
a steel (to keep them sharp)
I won't dare say that any brand is "the best" -- it all depends on what is most comfortable to you. I like Messermeister St. Moritz, but I also have some Global, Wusthof, Henckels, Furi. When I first saw KitchenAid, I liked them, but haven't really tried them. It's a very personal decision -- what fits your hand, what gives you the least fatigue, rocks the best for chopping, etc. I daresay everyone you ask will have a different preference. The nice thing is, there is no one right answer. You might even just try a cheapie, as long as it will hold an edge, because you can always get better knives when you have money.
As for luggage, as long as you protect the edges, you could even just wrap them in a towel! "The best" is what does what you need done, for the least money.
BTW, hasn't your school told you what you must have??