Interested in learning to crochet? Not sure what you'll need? Let me help!
Whether or not you think you'll be using these things for years, it's a good idea to find high-quality supplies. But that doesn't mean they need to be expensive. Take the time to hunt down some good deals on your supplies (here's a good idea: ask your grandma for hand-me-downs!).
Here is a list of the things you will absolutely, definitely need, and my comments and preferences:
(You will absolutely need these things.)
We have already discussed various weights of yarn, and how to read the labels. Now you need to put that knowledge into practice, and go find some yarn.
Now, you could, I suppose, drop by your local Walmart or equivalent "we have everything" store. Or you could go to a dedicated craft store with shelves full of various colors and styles. (I advise the latter, of course.) Wherever you choose to go, here is an important point to remember: You're a beginner. Those fancy yarns are not for you. Stick to simple, straightforward worsted weight yarn.
My personal absolute favorite yarn is Caron Simply Soft. It's worsted weight (so perfect for beginners), deliciously soft, and comes in beautiful vibrant colors. I make pretty much everything with Caron. (Now, this does mean I don't have a lot of experience with other yarns, so don't assume this is the best. It just happens to be my favorite.) I also love Red Heart's bright colors, although it's a little less soft.
Again, pick what you want and like.
I would suggest picking up a variety of sizes. Sometimes you need a smaller hook, and sometimes you need a larger hook.
I own a 3.5mm (US E/4; UK 9), 4.25mm (US G/6; UK 8-ish), 5mm (US H/8; UK 6), 5.5mm (US I/9; UK 5), and 9mm (US N/15; UK 00). I'll probably be filling in the gaps at some point, and I don't even know why I own the 9mm. That thing is huge.
The hook I learned with was the 5.5mm, which is a little bigger than most worsted weight projects require. The hook I use the most is the 5mm, although the 4.25mm is close behind.
If you only want to pick up a few hooks, I would suggest buying a pack containing those three sizes. (Those outside the US: match sizes as best you can, or ask the people who work in the yarn department what they would suggest.)
(You might not need all of this, but they're good to consider, especially if you have a few extra dollars in your crocheting budget.)
Safety pins: I have a plastic container with a snap-on lid containing a bunch of little safety pins. These little guys are good for marking important rows, or holding pieces together long-term. No pointy ends!
Straight pins: I also have a plastic container with a snap-on lid containing a bunch of straight pins. These are good for holding pieces together short-term, like while sewing squares together or holding fins to dinosaur amigurumi (that would be why I bought my straight pins).
Fiberfill or other stuffing: If you choose to get into amigurumi, you will need a lot of stuffing. Here in the US, you can buy a big bag of fiberfill stuffing pretty cheaply, and it'll last a long time. Be sure you have somewhere to store it, though.
Yarn scissors: Yes, you can just buy craft scissors if you like. I happen to like my yarn scissors because they cut yarn, embroidery floss, and thread quickly and easily. No sawing or hacking. They do their job, and they do it well.
Yarn needles: Buy several, because you will lose them! (I keep my three in a little jewelry bag for this reason.) Yarn needles have big eyes and aren't very pointy. They come in a variety of sizes, so be sure to buy one with an eye big enough to thread comfortably.
Embroidery thread/floss: These two things are the same as far as I can tell, but it's like soda vs. pop--a regional difference. This is good for making faces on amigurumi.
Safety eyes: These are harder to find unless you go to a craft store or order them online. They come in two pieces; one is basically a washer, and the other is a bolt with a half-sphere head. You push the bolt through the gaps between stitches and snap the washer on the back (don't play with them; they don't come apart). They come in a variety of sizes measured in millimeters, and you can easily replace them with buttons or embroidery if you don't want to spend money on the safety eyes. (They're really adorable though, if you do decide to get some.)
A craft tote: This should have been the most obvious thing in the world, but I almost forgot it. If you're a busy person who will take this hobby in the car or on the bus or train or subway, you'll need someway to transport it. I have a small bag specifically designed for crafts, with tons of little pockets and one large center area where I keep the skeins I'm currently working with. I know people who use large canvas totes and Ziplock bags. However you choose to transport your work, make sure you get it organized quickly!
I think that's about everything, although I may be adding to this list over the next few days. Now go out and find your crochet supplies! (And feel free to share what you got in the comments. I'd love to hear what kind of deals you were able to find!)