When I went through highschool, I had a TI 83 calculator. It was great and did everything I wanted to do. And trust me, I did a lot of math
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Obviously the TI 89 will be better than the TI 84 in terms of functionality. The cost is not really that different either.
So what you "should" be paying attention to is whether you can use the said calculator in various tests - such as the ACT tests. I saw in the reviews section that the TI 89 "cannot" be used in the ACT test. The TI 84 might be, check it out.
I remember writing a math contest in high school (I can't remember which one now) which allowed the TI 83, but not the TI 92, b/c of the extra features it had.
So,
1) Check whether the two calculators are allowed in various standardized tests - both in school and run by ministry/government/universities, etc.
I have a feeling TI 84 should be ok for sure.
2) Then worry about the price and functionality.