I had a short interest in street photography. It ended quickly because it was a gateway drug to one of my main interests: portraits. The reason I ended my candid street wanderings is because of how murky the trend became; It went from being stylish and cool with the Sartorialist to being pregnant with meaning and a bit exploitive with Humans of New York. Now, street photography is a huge propaganda machine for whatever liberal views are popular at the time, where the subject of the photo is a pawn for the greater cause. Street photography has always been this way, but the difference now is how amplified it is with the rise of social media. This powerful story-telling technique, in many ways, has become a fad, a way for a well off college kid to benefit from his "meaningful and powerful" pictures of a homeless man.
Anyway, that said, taking pictures of random people in the street is fun. I remember once when I was in Brussels during my street photography thing, I took a picture of a man sitting in a train while I was on the platform. The man looks at me, and shoots me the bird.
It's candids like this that the "greats" are known for, so of course it's the type of photography that many people want to get into when starting out. It's a great way to build your confidence about approaching people and getting out there as well. I would argue that street photography is the easiest form of photography; as long as you understand how to use your camera somewhat quickly it takes no time at all to pick up.
It also requires almost no gear.
All of the photos in this post were taken with my Nikon D3000 and the 18-55 kit lens.
This was even before my "prime-only" lifestyle, which started pretty soon after this.
So what do you actually need for street photography?
I don't know why anyone who is just starting out with photography ever spends more than $300 on equipment. Besides, cameras are so good now, that all cameras take an incredible picture. Why break the bank when technology allows for cheaper and easier to use equipment? If you're just starting, I'd recommend heading to the B&H Photo Used Dept, and find a cheapo DSLR. (This is where I buy most of my equipment)
Here's the thing about street photography: the line between you looking like just a photographer and looking like a perv is a thin one, so you don't want to be walking around with a ridiculously huge rig. If I were to get back into it, I'd be using my tiny Canon EOS M3, because only creeps take photos of strangers with a D800. This backs up my "cheapo DSLR" recommendation because you don't want to stand out.
As far as lenses, it's up to your preference. Get a 50mm lens or something that gets in tight, but is great for portraits. Lower end primes also tend to be small on your camera, shrinking it down a little bit instead of sticking a telescope on the end of it. A kit lens that comes with your camera works just fine as well. Really there's no wrong answer, almost anything works. You just may have trouble with say, a fisheye or something.
Here's the gear you actually need for street photography:
Camera, preferably cheap/small. Mirrorless cameras are getting pretty perfect for this if you can find an inexpensive one.
Lens, in my opinion, a 50 mm or something good for portraits that you don't have to worry about zooming with. Don't get a telescopic perv lens.
If you don't want to buy either of those things, use your smartphone. If it's capable of taking photos, it'll do.
That's really it. Street photography, if anything, is a great composition exercise. If you can get good and fast at it, I believe it can bump your photography skills to the next level.