The minimum resolution depends on the distance at which you expect the camera to detect objects. There is no universal minimum resolution that will satisfy all scenarios.
The same camera model in the same environment will have different minimum resolution requirements depending on the lens that it is equipped with.
When configuring a camera take screenshots and measure how many pixels an object of interest occupies at the maximum desired detection distance. If the smallest dimension of the object occupies less than 30 pixels you need to either increase resolution or change to cameras with a narrower lens until the object occupies at least 40 pixels.
This is the most common reason why object detection fails. Illumination of the scene varies drastically from day to night, from sunny areas to shade zones so balancing the contrast can be a fairly challenging task. There are certain recommendations though that will allow you to achieve the optimal image contrast to maximize object detection efficiency.
1. Decide which parts of the image are important and which can be over/underexposed. Often part of the image will be capturing sky or distant background that are not important for surveillance but can be influencing how the camera automatic algorithms adjust exposure. This can cause over/underexposure of the important parts of the image thus WDR or Wide Dynamic Range if available should be used to fix this problem as it allows the camera to selectively increase the contrast of some parts of the image while keeping bright areas still not too bright.
2. If the camera does not have WDR or the produced results do not provide good enough results manual exposure and brightness/contrast settings should be used. In general, better results will be achieved for high contrast images rather than soft and blurry ones.
3. Another important camera parameter is sharpness. With less sharpness, the image might look smoother for the naked eye but due to "soft" edges of the objects precision of object detection will be lower than for a sharper image. But too much sharpness can increase noise thus the number of effective pixels will be decreased. In general, sharpness should be increased until noise starts to appear.
4. Placement of the camera can also render object detection useless if there is a tree or a bush blocking the main path that people are walking on or if the camera is looking at odd angles obscuring the real shapes of the objects. For example, in this scene, the pathway is partially blocked by the bush so a person walking in front of the camera will be mostly hidden and thus unrecognizable.
And the bellow example demonstrates how the person will look if the camera is positioned too high and is looking straight down. Here again, the shape of the object is barely recognizable as a person, and as such the reliability of Object, detection will be low.