I would not consider the example you are posting as a long exposure. It looks frozen, so in my opinion is 1/100s or faster.
Yes, it is very grainy, so they are using a high ISO, and yes very large aperture.
Again you need to test what kind of style you want. You must decide between the style and the capabilities of your camera.
These "long exposures" will depend not only on the speed of your subject, but also on the focal length you are using, except in the case when you are using a tripod.
A good relationship on the lowest speed you can use, to avoid your own shake, is that focal length and shutter speed should have the same numbers. E.g., if you are using a 50mm lens you can safely shoot at 1/50 sec. If you are using a 200mm lens, you need like 1/200. Of course if you are very good you can reduce your own shake, perhaps say 2-4 times.
If you are actually using a tripod or a very firm support, I would make some tests photographing a friend waving something.
You can try shutter speeds below 1/15. 1/8 or 1/4.
If you combine the long exposure with a flash try to configure your camera with rear curtain sync. If not the subject could appear to be moving backwards. But that can be interesting too.
In the end: you need to do some tests. Do them methodically.
One more thing: As this grainy and very high contrast photo is interesting you can underexpose the photos, and then adjust the output in post production. This will magnify the grainy look. In black and white would be interesting... In colour will depend on your sensor.
Shoot in raw.