We study four dimensional SU(2) lattice gauge theory in the Hamiltonian formalism by Green's function Monte Carlo methods. A trial ground state wave function is introduced to improve the configuration sampling and we discuss the interplay between its complexity and the simulation systematic errors. As a case study, we compare the leading strong coupling approximation and an improved 4 parameters wave function with $1\ifmmode\times\else\texttimes\fi{}1$ and $1\ifmmode\times\else\texttimes\fi{}2$ plaquette terms. Our numerical results favor the second option.