A couple of quick things (I am writing as someone who practiced international arbitration at a big firm and now practice it at a boutique; I intended the former and not the latter):
--It is reasonably difficult to break into this. Both practices are generally prestigious and popular, meaning there is a a lot of competition. You have to have great grades and come from a good school (T14 generally), or have a very good command of Spanish, Portuguese, French, Chinese, Korean, etc. There are exceptions to this (see, for instance, professor Susan Franck, who had a great career in international arbitration before teaching, http://law.wlu.edu/faculty/profiledetail.asp?id=267), but most international arbitration practitioners have fancy-pants degrees and are tre cosmopolitain.
--Note that International Trade (which is a specialized set of rules) is quite different from International Arbitration, which is mainly commercial litigation without many rules. I do not know much about international trade except as an American probably the best job you can have in trade is to work at the US Trade Representative's office as a lawyer.
--Most of the jobs in these areas are at big firms. Chambers & Partners lists most of the usual suspects: http://www.chambersandpartners.com/USA/Editorial/71007. But in short, the top of the game in the US include Debevoise, White & Case, Wilmer, Freshfields, King & Spaulding. Many good firms, but no guarantee you will get international arb work if you ask for it.
--I could point you to a couple of boutiques, but the prominent one is
chaffetz lindsey llp and Astirraga Davis (I never could spell that right) at http://www.astidavis.com/.
--I think an interest in international work is important for your 1L summer. If you can afford to do something in the summer between your 1L and 2L years that is public interesty in another country and in another language, and/or some sort of job with the UN, human rights group, or a regional body (the EU, Organization of American States, etc.).
Mind if I ask what language you speak? Why assume it? The "in-demand" language can cut a couple of ways. A lot of people speak Spanish, and some people you are up against have native. Sometimes, however, it pays to know a slightly less in-demand language that is commercially useful (for me, I learned Portuguese, and that has helped immensely). But there may not be much you can do about this if you are starting law school in the fall. If you don't have a language already, you might wait until you are done with 1L year because it is intense enough.
Feel free to write me directly if you have more questions (or post them here); I'd be happy to help.
--Larry, the
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