When I’m out for a day of street photography I bring my regular backpack with Fujifilm x100s or Canon crop body with 30mm Lens on it. Smaller camera systems are less obtrusive than big and heavy DSLRs. They are easier and less painful to carry around, especially when taking long walks.
In terms of street photography, less is more.
Everyone wants to become invisible when they are on the streets. Using a small camera makes this much easier to do.
I like to use prime lenses. My favorite two focal lengths are 30mm and 50mm on my cropped sensor cameras. Prime lenses tend to be smaller than zooms. Most important thing is , to get used to your lens focal length and you should be frame ready all the time. As street moments happen quickly, your frame must be ready to capture the moment.