I'd really suggest starting simple! You don't know yet how you're going to like it set up, or if you'll like it at all, so best not to invest heavily, or get a journal that's so pretty that you'll be upset with yourself when you inevitably make mistakes, or perhaps have an entire first few months of spreads that you dislike later down the line.
Firstly, keep in mind you could use anything. A cheap composition notebook and a Bic you accidentally pocketed off the counter of your doctor's office will do. ;)
But I assume you mean, what do people typically use.
I'd start with a good pen -- Sharpie pens are actually pretty nice and readily available in most stores, from Target to Family Dollar. I still use them exclusively 8 months into bullet journaling, simply because it's easy to get more on the fly if I need. A lot of people also like Microns (so do I -- I've used them in the past for drawing), and those are typically found either online or at art stores.
For a journal, a dot grid notebook is the usual choice. And you know, a lot of people swear by the Leuchtturm1917, but I'm gonna commit bujo blasphemy and admit I don't personally like them, and I don't recommend them for a beginner. The pages are thinner than most dot grid journals and they can be unforgiving of hesitant or heavy pen strokes. Also, they're really expensive. Like, 20 bucks expensive. You can find a nice-looking and good quality dot grid journal for so much less. Here's a couple I found off the bat, for half the price, on Amazon. And both have really good reviews, too.
I'm kind of a DIY'er, so I actually made my own softcover bujo with replaceable pages. But I'm OTT like that. ;)
That's all you need, really. A pen and a journal. I find having a couple of highlighting colors is nice as well. I have a handful of Tombow pens and I find that's all I need, but they are pricey. For just highlighting, a regular highlighter is an equally good choice.
Hope this helps!