Pseudo 1st and 2nd order are "the usual suspects" that you look at first for almost any kinetic reaction analysis. If first order fits it might actually be a first order reaction, Second order is more often a convenient form of a correlation that might be fit for purpose. 0.5, 1.5 order are also often looked at to help correlate the data.
Simply we get idea about the the rate of removal.Further knowing values of the rate constant one gets idea about the rate of diffusion .Usually it has been seen that second order fits well as compared to the first order.