The recommended calculators listed are the models I recommend since they all have very similar features and key lay outs. They are also allowed on the SAT and ACT exams and are some of the most widely used calculators in college math classes. In addition, the software that I use in class to demonstrate calculator usage is a simulator of a TI-84. The main differences between them are quite minor and include whether they are rechargeable, have a color display or can be connected to a computer for upgrades. Some students have been able to find used versions of these to save money. The TI-82 is rare but if you stumble across one that still works it has a similar key layout to the 83's and 84's.
A little warning... There are a lot of great calculators available today that are fine products but have presented problems for students in my classes because the key layouts are quite different and the extra features are far beyond the scope of high school math and interfere with what students need to do. Some examples are the TI-nSpire and the TI-89. It is also worth noting that some models of these calculators are not allowed on all standardized tests such as the ACT. I have also seen students struggle with Casio calculators since the key layouts are extremely different than any Texas Instrument calculator.
If you have recently purchased a calculator that I do not recommend I would exchange it for a recommended one (they are usually cheaper as well). However, if this is not an option it is still okay to bring these calculators since they are actually fine devices. Just be prepared to spend extra time learning how to use them. Most common tasks are explained well with a quick Google search. I may only be able to help outside of class time (before/after school or lunch).