Working out the focal length from the distance and field of view

There is no "recommended" distance for any lens. The focal length you choose depends on the field of view that you require and your distance away.

It is easiest to visualise what is going on by thinking about a pinhole camera: The basic rule of perspective can be deduced from the geometry of this diagram:

$$\frac{\textit{Object size}}{\textit{Image size}}=\frac{\textit{Object distance}}{\textit{Image distance}}$$

For a camera with a lens, the image distance is approximately equal to \$f\$, the focal length of the lens, so: $$\frac{\textit{Object size}}{\textit{Image size}} = \frac{\textit{Object distance}}{f}$$ The horizontal field of view is the width of an object whose image exactly fills the sensor from one side to the other.

The sensor for a full-frame camera is 36mm wide. For a camera with a crop factor of 1.5, the sensor is \$\frac{36}{1.5}=24\$ mm wide.

So, for a field of view that is \$x\$ metres wide horizontally, at a distance of \$y\$ metres, you need to use a focal length of \$f\$ mm, given by this formula for a FF camera: $$f=\frac{36y}{x}$$ or by this formula for a 1.5 crop camera: $$f=\frac{24y}{x}$$ This assumes that the camera is used in landscape format (the horizontal dimension is greater than the vertical dimension).

For example, if you are using a 1.5x crop camera and want a field of view that is 3 metres wide at a distance of 20 metres, then you need to use a focal length of \$\frac{24\,\times\,20}{3}=160\$ mm.

Of course, if the focal length is decided already (because it is the only lens available), then you can work out the distance away you need to stand to obtain a certain field of view for your 1.5x crop camera: $$y=\frac{fx}{24}$$ For example, if you want a horizontal field of view 3 metres wide and the focal length is 300 mm, then you need to be at a distance of \$\frac{300\,\times\,3}{24}=37.5\$ metres. Again, this is for a 1.5x crop camera.