AskScience

While smartphones and computers have become serious competition for graphing calcs, academia's slow to adjust, so they'll be your only option for a good while if that's part of your path. Because of this, it's definitely worth getting comfy on one and there's countless videos online. As far as the specific one, that's totally your choice. The more obscure it is though, the harder it gets to find help with the more intricate applications. TI-8X's are nice as even classmates or friends can lend a hand. But graphing calcs have been and will be the only way to take a math course, the choice is yours when it comes to which one you want to though, but it helps to choose wisely!

There is probably a (weak) argument for using them in examinations, as an independent learner however you can probably just get an app on your phone to do it all better and faster. I don't think you are shortcutting anything by going straight into programming, though it might slow you down compared to something more user friendly.

Whenever I went to college for engineering I used a basic scientific calculator. Googling around I believe that the TI 36X Pro may have been the model. I never had any issues with it. It couldn’t graph, but if I needed plots I would do them with a programming language or excel depending on the context.

Graphing calculators definitely aren’t necessary.

Against the current: I studied pure math and didn’t use any way to automatically graph anything until my master study. So you don’t need any method to graph stuff. That doesn’t mean you should do without, just that you can.

I think that by now an app on your smartphone would be best, since it would require little to no initial investment. Or you can ramp up on computer programs, such as wolfram alpha (website), or matlab (licensed program, probably not worth the money). If you like programming, sooner or later you’ll probably end up on Python.