I work for a large finl services firm in the LegalCompliance dept. I have responsibility for covering our international branch offices. This means I'm in either Europe or Asia about once per quarter. My "specialty" is securities law, more particularly investment advisory. I think with the proliferation of hedge funds and private equity and other US type "products", this area will continue to grow.
I don't think attending law at LSU will convey any particular advantage, or disadvantage for that matter. While civil law is prominent in some European jurisdictions, my experience has been that common law is, well, pretty common. In my particular area, I've noticed that a lot of foreign jurisdictions actually look to US practice when formulating rules and regs for their capital markets, etc. In Europe, there's a good amount of momentum towards harmonication (do a google search on MiFid), so I think that barriers to practice will continue to recede.
I took a course in aviation law when I went to law school. It was pretty interesting, and much of aviation law precedent comes from shipping law. As I recall property right issues are huge, and liability under the Geneva convention too. I went to school pre 9/11, so I can't comment on how things have changed since then.
In order to land the best law job possible, your priorities should be, in order:
1) Getting into the law school of your choice. I.e., keep your grades up and prep well for the LSAT.
2) When you get into law school, do everything you can to keep your grades up. Also participate in law reviews, journals, etc should the opportunity present itself. I'm not familiar with LSU, but if they publish some sort of transportation law journal, that would be a good one to shoot for.
Finally, one piece of insight I would pass on to any person considering a career in law: be prepared to work like a dog. Long hours are expected, and you won't have much time to do much of anything else. You'll make decent money, especially if you land a position at a large law firm, but it's really blood money that they're paying you. That said, law can be a rewarding career - but go into it eyes open so you don't get disillusioned like a lot of young attorneys do.
Good luck !