I used to shoot a lot of street, and it's still my favourite type of photography to do for fun. I started with a 35mm lens on an APS-C body. That was already a bit too long, so I got an X100 which was perfect at 23mm (35mm Full Frame equivalent). I recently got another APS-C body with a 35mm lens, but ended up having to get the 23mm as well since I prefer the length.
50mm would be much too long for me, although I could see 40mm being good. As others have mentioned, it being a pancake would be very convenient to carry around.
A good way to find out what length would be good for you would be to use your 18-55 zoom lens for some street, then go home and look at the EXIF data to determine what the focal length was for your favourite shots. In Lightroom, hit the "I" button on your keyboard while having an image open to show different information. I only have experience with Lightroom, but I'm sure other programs can show it, too.
You also might find out that you prefer shooting with a zoom lens. I have a friend who shoots excellent street photos with an 18-200 or something on his Nikon. I only shoot with primes, but that's a personal preference.
I wouldn't worry too much about focus speed. A common technique with street photography is to zone focus to about 2 meters, then set the camera to f/8. Everything between 1 to 4 meters or so will be in focus.
Of course, all of this depends entirely on what your personal style is, which you may still be developing. Again, go out and experiment with your zoom lens!