It frustrates me when someone says 'you should do it this way', as if there's only one right way and everyone should do the same. If that sounds like a life philosophy and I don't like to be told what to do, well, yes, that's probably true. But especially with a creative endeavor, some techniques might be helpful but how dull and limiting if we all took the same approach. It comes up often in street photography. Use a wide lens, get close, use a small camera. The latest I came across recently was a blanket recommendation to use an aperture of f/8.
The argument for f/8 was that almost everything would be in focus (not true in most cases), and that lenses tend to have a reduction in quality at their widest and narrowest apertures (more true, but rarely a concern for street photography where the story or emotion are usually more critical to the image than precise details).
There are plenty of settings you could use for street photography, or candid photography in general because the same principles apply for capturing candid shots at a wedding for example. Some will work better for certain situations or with certain cameras or lenses, but also with the style of image you want to capture.
The aim of zone focusing is speed, to manually focus in advance so that you only have to compose the image and release the shutter at the right moment. To do this, you first decide in advance what distance away from you, roughly, your subjects are likely to be. You then set an aperture and manually focus the lens so that your subjects will be in acceptably sharp focus at that distance (the aperture and focus distance depends on the lens).
f/8 or f/11
f/8 or f/11 may well be a suitable aperture to use for zone focusing, giving a reasonably wide depth of field. But don't consider it a rule that you have to stick to.
Shutter Speed Priority
Zone focusing is about speed and maximizing your chances of capturing a brief moment, whereas shutter priority and aperture priority are about making some creative choices. You could use shutter priority if you want to make sure you're removing any motion blur from the scene, or indeed if you want to intentionally create some (such as for a panning shot).
Aperture priority is taking control over the depth of field. Sometimes you might want to isolate a subject, sometimes you might want the background to be clear. One potential issue to be cautious of though is in bright conditions, where your camera may not be able to achieve fast enough shutter speeds to use a wide aperture (i.e. the images will be over-exposed, even at the maximum shutter speed).
Of course there's no reason why you shouldn't control both the aperture and shutter speed. Adjusting both rapidly to respond to a situation is difficult though, so you could use auto-ISO to allow you to adjust one setting without altering the overall exposure.
I use aperture priority most of the time, except in low light when I'll generally switch to manual to deal with the conditions and make sure I have the minimum shutter speed I want. Of course I miss a few shots because I'm too slow. That will always be the case. Using a wide aperture makes it more likely that I'll miss getting the focus spot-on sometimes, but I'm fine with that if it means getting the images how I want them the rest of the time. That's my preference for how I shoot. Most often I like to have a specific focus on a subject and not on the background.
You might prefer to keep much more of the scene in focus for your shots. You might want to manually focus or even prefer using a manual lens. Whatever you choose though, choose because it will give you the results or experience you want, not because someone tells you to do it. Then practice until it becomes second nature.