Many very senior people in international affairs are lawyers, but law school is probably not the most efficient way to start a career in international affairs. Law school is three years of a curriculum which is mostly irrelevant to international relations. It is difficult to get into good law schools, and there is usually no financial aid except for loans. The current surplus of lawyers means that law school graduates are now having serious trouble getting jobs. It is true that students may be able to get an interesting non-legal job with a law degree, since employers figure they must be reasonably intelligent if they have survived law school, but there are other alternatives. If students want to be a lawyer, go to law school. If they do not, they should think seriously about the alternatives.
There is a good deal of confusion about international law as a career. It is convenient to divide international law into public and private. Public international law is concerned with whether or not the behavior of governments corresponds with international law, whether the American invasion of Panama was legal, for example. This is what the term international law means to most people, but there are very few institutions which will pay people to do such analysis. The State Department keeps about eighty lawyers on staff for this purpose, but most of the other people in the field teach in universities (probably as many in political science departments as in law schools).
Most international lawyers are concerned with private international law, how individuals and corporations can carry on transactions within different and sometimes conflicting legal systems. If a tanker registered in Liberia and owned by a company in the Bahamas carrying a load of oil owned by an American corporation hits a Russian submarine and dumps its oil onto Belgian beaches, who pays what to whom? Private international law is popular because people and organizations will pay money to get answers to these sorts of questions. This kind of work, in turn, sometimes leads to other things; international lawyers often serve as representatives for multinational corporations to the public and governments, a kind of business diplomatic corps. Nonetheless, international law is a fairly minor branch of law, and this is reflected in law school curricula; if studetns take two international law courses in three years, they will be doing well. (The University of Iowa seems to be an exception; it is advertising a more extensive program in international and comparative law.)
Law school is the best alternative for anyone who wants to practice private international law, but students must remember that they must be a lawyer first and an international lawyer second. If they want to study public international law, students may actually do better in a Ph.D. program in political science specializing in international law, although there are very few places in the U.S. where this is a serious alternative; their career will presumably involve working in a university as a teacher-researcher, either in political science or, less likely, in law school.
There is no pre-law curriculum in the United States; essentially law schools will take students regardless of their major if their grade point average and law board scores are high enough. Inasmuch as curriculum makes a difference, they prefer students with broad interests in the liberal arts and tend to frown on pre-professional degrees. In particular they recommend that students do not take law courses before they get to law school, arguing (probably correctly) that other institutions will just teach them incorrectly and that they will have to undo all the damage others have caused. However, anyone interested in law school should take one course which requires intensive reading of cases, just to see if they can tolerate it for three years, since that is what they will do in law school.