I worked there. On almost any item, I would try to dissuade you from Best Buy's extended warranty. Laptops are one of the few exceptions. The biggest reason I can think of to actually buy the extension is the laptop's battery. If it displays a decrease in average life by the end of the warranty, they'll replace it free of charge. They also cover dead pixels and a variety of other issues that the manufacturer typically would not service.
If you weren't attending LS, I would really try to talk you into an Apple. The early poster's experience certainly hasn't mirrored mine. I've got a 12" iBook, the very bottom of the line, and I love it dearly. It's stable and fast, the operating system is intuitive, and I've yet to find anything that I could do with a PC that I can't do with the Mac. The only exception is law school exams, which at most schools require a PC running Windows XP. Darn.
You'll hear a lot of people arguing for one brand or another, but the truth is that all laptops are pretty darn similar. I would honestly buy the cheapest one that fits your needs. The biggest tasks driving hardware development are media editing and games, and it doesn't sound like either of those are priorities for you. Even something relatively low end should work out fine for all three years.
Dell has a lot of brand recognition because they advertise incessantly. They probably aren't the best value available. Their machines are pretty good, basically the same as anyone else, but my experiences with their customer support have generally been pretty terrible. The big advantage of Dell is that since they sell so many machines, replacement parts are widely available and relatively inexpensive. The same can be said for Compaq/HP. Big volume has its advantages.
If I was going to recommend any one brand, I would probably steer you toward eMachines. Their early machines were, without exception, the worst computers in the world. Seriously. They were terrible. Sometime in the last few years, they really cleaned up their act. If you check out Consumer Reports, epinions, etc., I think you'll find that eMachines is one of the most consistently highly rated brands in terms of customer support and value. And, happily, their machines are ridiculously cheap.