DigiPen and Full Sail are trade schools turned Universities, they do seem to produce many highly competent graduates who go on to success in the industry, but that doesn't mean they are the best path to a career as a game programmer.
Considering your specific needs I wouldn't worry too much about which school, the truth is any credited US college with a good Computer Science program will suffice. If you want to get to do the 'fun' work (game engine design, which also pays the best) you should major in Computer Science and minor in Mathematics.
I will add a caveat to this; while the most demanding programming jobs in game design require knowledge to perform application of higher level math and physics, the truth is all commerical game projects require a very large talented team of people and not all of the programmers will even have college degrees. You'll find all skill levels in programming, from Jr/Apprentice level up to Sr. Software Engineer. Unfortunately most of these folks are considerably underpaid for what they are doing compared to their business software developer counterparts. Often the Jr. programmers get to work on script code and closely with the level designers. These guys actually create the game. The more Sr. programmers design and maintain the 3D/physics engine that's used as a foundation for any number of games the publisher might have in the works. This means in the larger studios the brightest programmers don't get to design games they create, they just build the foundation and create all the parts the less Senior programmers will use. Smaller studios will often license a third-party game engine, sometimes to the extent that Sr. Programmers aren't even needed on a project (this is still rare as most companies that license will require senior programmers to extend the game engine).
I don't want to discourage anyone from doing something they are passionate about, but you may want to read about some the recent disputes between programmers and the big game publishers (Electronic Arts). While video games have become huge extenshion of the US entertainment industry (even more profitable than the music business as of a few years ago) it seems as with many publicly traded corporations, everyone is trying maximize profits at the sake of the quality of their product and the treatment of their staff (save for those at the top of course) Electronic Arts and Activison-Blizzard really own the industry and they are very competitive and both have their horror stories.
I believe the age of the rock-star/artist game programmer (John Carmack, David Perry, Shigeru Miyamoto, Peter Molyneux, etc...) is come to a close. If you want to design video games for the art of it your best bet will be to target a platform where a small team can do-it-all such as the Apple iPhone or the Microsoft XNA Creators Club for XBox 360. The information needed to approach these platforms is widely available and one doesn't need a math or computer degree to purchase the books and self-train. If you are not the self-training type my advise would be to stay away from any software development job or any technology related field in general as with any technology after your formal education you will continue to be expected to self-educate or you will find yourself unemployable.
Independent game studios will pay even less, but you're the type of programmer that's more right-brain than left you'd probably do better there as they will provide more freedom (unfortunately the smaller studios are also a lot more unstable and always in start-up mode)
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