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Some math professors don't let you use calculators on exams/quizzes/etc. The physics/chemistry professors usually do, however. Most students have a calculator that can at least do graphing/matrices just in case.
You won't need a calculator for any Calc classes (and you probably shouldn't even use them outside of class no matter how tempted you are.) If you have the money/can find a cheap one I'd go for the TI-89. (Just because they make some classes easier and you may want to get used to it for a bit.) But a TI-84 (or any similar graphing calculator) will be just fine. At some point, you may need a simple non-graphing calculator. But you can find those for ~$10 in the bookstore and cheaper other places, so don't worry about those.
A majority of classes only allow calculators up to a TI-36, especially architectural engineering classes. That is the highest level calculator allowed for use on the FE Exam, so that is where the standard comes from.