  We investigate the properties of the stochastic Gross-Pitaevskii equation
describing a condensate interacting with a stationary thermal cloud derived by
Gardiner and coworkers. We find the appropriate Ehrenfest relations for the
SGPE, including the effect of growth noise and projector terms arising from the
energy cutoff. This is carried out in the high temperature regime appropriate
for the SGPE, which simplifies the action of the projectors. The validity
condition for neglecting the projector terms in the Ehrenfest relations is
found to be more stringent than the usual condition of validity of the
truncated Wigner method or classical field method -- which is that all modes
are highly occupied. In addition it is required that the overlap of the
nonlinear term with the lowest energy eigenstate of the non-condensate band is
small. We show how to use the Ehrenfest relations along with the corrections
generated by the projector to monitor dynamical artifacts arising from the
cutoff. We also investigate the effect of using different bases to describe a
harmonically trapped BEC at finite temperature by comparing the condensate
fraction found using the plane wave and single particle bases. We show that the
equilibrium properties are strongly dependent on the choice of basis. There is
thus an optimal choice of plane wave basis for a given cut-off energy and we
show that this basis gives the best reproduction of the single particle
spectrum, the condensate fraction and the position and momentum densities.
