usually fungal life cycle wents upto 14-20 days, so whatever your objective is you have to select the parameter within this period.
from day 1-last day, you can check dry weight of fungi, pigment production, enzyme production, and if your study goes on deeper, gene expression also you can check with change in time.
As Stephane Dagnas noted there are a number of different methods based on what you want to determine. One other method for examining mycelial growth is a "race tube". This works better than a plate for fast growing fungi which may fill the plate quickly. Because growth rate, particularly for the first day after transfer and when nearing the edge of the plate, can be variable, having a longer time measuring linear can be useful in some cases. An example of this type of test can be found at http://www.fgsc.net/neurosporaprotocols/How%20to%20measure%20and%20monitor%20line%20final.pdf. The type of medium to use will depend on your organism and the questions you are interested in.