How to estimate radial distortion from lens characteristics?
There is a lot of variability because distortion can be compensated for optically and lens designs differ. Some lenses are marketed as rectilinear, most not. You would be making the distortion worse for some lenses by doing any correction advised by focal length alone. For focal lengths shorter than about 30 mm, the distortion seems dominantly barrel, according to the data of:

Neale, W., Hessel, D., and Terpstra, T., "Photogrammetric Measurement Error Associated with Lens Distortion," SAE Technical Paper 2011-01-0286, 2011, doi:10.4271/2011-01-0286.

They only tested zoom lengths though.