Question

how wavelength and frequency are important in determining the type of light.

Answer 1

Because light is c = wavelength * frequency
we already know c: the speed of light in empty space and it does not change.

if we know the frequency we can compute the wavelength with wavelength = c / frequency

if we know the wavelength we can compute the frequency with frequency = c / wavelength

The wavelength determines the type light:

short (or small) means energy like x-rays or gamma rays

medium, that's light we can see

long, radio waves, used by your cell phone to communicate with antennas.