If you want to shoot street photography, all you need is a camera. Any camera. My suggestion is to have an inconspicuous small camera, a smartphone , a compact camera or a mirrorless camera. You can even use a film camera or a bulky DSLR. It really doesn't matter as long as your camera has a shutter button.
However, there is a saying, that the best camera is the one that's with you. So if you think about that, the one camera, that you always carry with you, obviously is your smartphone. The big advantages of smartphones are that they fit in your front pocket and are not obtrusive due to the fact, that everybody out there uses a smartphone camera in the public.
Personally, my go-to street photography camera is my FujiFilm X100T. It is a small mirrorless camera. But it is definitely not inconspicuous. People notice it as soon as I bring the camera to my eye. However, the biggest advantage of the X100T is its portability, sure, it will not fit in my front pocket but I can put it in my jacket pocket. Also the shutter is super silent. I never had anyone taking notice of the shutter sound of my X100T. When you're shooting with a DSLR people will most probably take notice of the shutter, you have to take this into account and consider shooting with an electronic shutter, if available.
Another thing is that most cameras nowadays are capable of shooting high ISO (when it is getting dark, high ISO values are necessary to keep the shutter speed at acceptable values), ten years ago ISO 640 was luxury. Nowadays ISO 6400 is no problem at all.
Maybe smartphones are somehow limited with their ISO capabilities; on the other hand, you can use this disadvantage and adjust your shooting to this drawback.
When it comes to autofocus, just forget about it. It's one of the most overrated topics in photography. Some brands advertise their cameras with being able to shoot 11 pictures per second with autofocus. All this stuff is not needed in street photography. The autofocus of my X100T is not the fastest in the world, it is rather slow. The workaround is to focus manually- or even better, use the zone-focusing technique (if you're not aware about this, check out this link). Zone-focussing basically transforms your camera into a point and shoot; hence, you can focus on composition instead.
What about bokeh?
In the picture above, you can see what bokeh looks like (it is the blurred background in the out-of-focus part of the image), I focussed closely to the ground and therefore the overall part of the picture is out of focus.
I tell you right away, it is not essential. When I started with photography, I thought bokeh is the most important thing and this effect "makes" better pictures. After three years, I came to the conclusion that bokeh makes you lazy in terms of composition. If the main subject is isolated, you lose the ability to tell a story with your picture due to lack of surroundings. More importantly, you have to pay way more for your lens to get a decent bokeh. In the picture above, I stopped my lens down to f2.8, as you can see, even at f2.8 you can produce a nice looking bokeh if you need to.
Does size really matter?
Yes, it does in street photography. As I stated above, the best camera is the one that's always with you. The bigger the camera, the less you take it with you. Also, consider that a bigger camera makes you a whole lot more conspicuous. As a street photographer you should blend into the background like a stealthy ninja.
If you're like me and hate carrying around a heavy camera, look out for a tiny point and shoot or just stick with your smartphone.
So does your camera matter in street photography?
Even though smaller cameras are less conspicuous in street photography, you can basically shoot with whatever you have. The most important thing is, that you feel comfortable using your camera.
If you plan to buy a new camera- only do it if your current camera really limits your creativity. Just be aware that a new or better camera doesn't make you a better photographer. I can speak from experience.
I hope this blog post could inspire you to just start street photography with whatever camera you own at the moment.
PS: two of the images in this post were shot with my smartphone.