Hi Mr. Gabe,
Street photography can be done with any and all lenses. The classification refers more to they kind of images and the style of shooting, than the tech used to create it.
Some believe that Street Photography require the shooter to get up close and personal with the subject matter, to really count. Others focus more on the composition and the subjects.
Common to most schools of thought is the idea that you walk around and observe what happens, then takes the shots very quickly in the hope that you catch something authentic and original. For that reason, many street photographers set their lenses at a hyperfocal length, giving maximum DOF. This allows you to shoot very quickly without having to wait for auto-focus.
The Nikon 35mm F1.8 is a classic street photographer's lens - in fact, I believe Nikon made this to commemorate Henri Cartier-Bresson who is one of the pioneers of street photography.
But there are no rules of course - some use zooms, others use cell-phones, rangefinders, lomo-cameras...whatever works.
But if there is any common thread - lens-wise - in street photography, it's the idea of speed. It's impulsive, intuitive and largely a "shoot from the hip" approach that favor candid shots. And for that, the 35mm is excellent.
Good luck with your choice!