Equipment
I am a big supporter of the idea that you do not need any fancy supplies to make good art, and this is true here. The most you need to get started is a needle, some yarn, and determination.
This being said, I have some suggestions. I recommend starting with a cheap needle to make sure it is right for you, as crocheting stuff can be pretty expensive. Once you know you're into it, there are many options! See below for specific categories.
Needles
I would discourage getting thin needles (where you hold it), wooden needles (unless very high quality), or ones that are overly decorated. This is because those needles aren't as functional. Plastic needles are okay, but don't last as long and may cause irritation for sensitive hands. Metal ones are hard to hold for those with dry or sweaty hands. My personal choice is metal ones with a grip, as they are comfortable with joint pain and dry hands. When getting needles, note what size they are. It is important to get yarn and needles that go together with each other and the project you're making.
Yarn
Any yarn can be used, as well as string, ribbon, or thread (if you want to take that on, but please don't). A good starting yarn is the cheap red heart yarn at craft stores. However, I wouldn't recommend long time use as it irritates the hands. You can soften it with tutorials. There are many low, mid, and high end yarns. What you use is up to you, but it is worth noting cost, how much yarn is needed for a project, sustainability, and difficulty level. For example, really big yarn is good to use as a beginner as it's easier to manipulate, whereas yarn that is loose is harder to crochet well.
Other
There are many other great tools you can use in your journey! Some of my favorites are a smooth wooden bowl for small yarn projects, a spinning yarn holder so you don't have to manually turn the roll, and a crochet kit (with needles in every size, row markers, yarn scissors, and yarn needles). Get what you need, want, or will use, but know that it isn't the tools that make the carpenter. These can be helpful but you can be just as good without them!