I know it is confusing, but transmission lines have to be modeled with respect to the frequency range you are using them in. A wavelength is the physical length one period of your frequency. In a PCB, a shorter, because the PCB dielectric material makes the speed of light slower.
So you need to calculate a wavelength in your board material for the highest frequency you are interested in. If the length of trace you are using is << than one wavelength (say ≦ 0.1 wavelengths or shorter) then you can model the transmission line as a lumped element effect. (although modeling it as a transmission like still works 100% fine too).
If, however, the trace length is ≧ than 0.1 wavelengths, you really should only model it as a transmission line. If you try to model this longer line as a lumped element effect, you will have very big errors.
The characteristic impedance is a ratio of the electric field/magnetic field, which is a real number for lossless lines, and almost a real number for lossy lines. Just think of it as either 50 or 100 ohms, respectively...with no imaginary part.