The honest list
You need a way to heat water, a vessel to brew in, and a way to separate leaf from liquid. That is the whole requirement. A mug and a basket infuser will make a good cup of nearly everything, and the gap between that setup and a very expensive one is much smaller than the gap between using the right water temperature and not. Anyone who tells you otherwise is describing a hobby rather than a drink, which is a legitimate thing to describe but is not the same thing.
What actually changes the cup, in order
Water temperature comes first by a wide margin, then leaf quantity, then steeping time, then the water itself. Equipment appears well below all four. A gaiwan does not make better tea than a mug; it makes tea faster and in smaller volumes, which lets you steep the same leaves many times and notice how they change. That is a different activity, not a better version of the same one.
Where spending money does help
Two places. A kettle you can set to a temperature removes the single most common error, though a thermometer or simply waiting achieves the same thing for nothing. And a vessel that pours cleanly and completely matters more than what it is made of, because leaf left sitting in hot water keeps extracting and the second cup pays for it. Beyond those, you are buying pleasure rather than flavour, which is fine as long as you know which you are buying.
What to skip at the start
Yixing clay, which is unforgiving and should be dedicated to one tea type. Anything described as a tea set on a general marketplace, where the pots frequently pour badly. Fine-mesh balls that cramp the leaves into a space they cannot expand in — the single most common piece of equipment and the one that most reliably makes tea worse.