Certain discretizations of second-order elliptic stochastic partial differential equations in primal or mixed formulation, where the diffusion coefficient is modelled via a truncated Karhunen-Loève expansion, result in a sequence of linear systems. We employ Krylov subspace recycling methods that utilize information generated during the solution of a previous system in order to improve the convergence behaviour of the next system. In particular we discuss the ordering of the (independent) systems. In addition we report on our experiences when using Krylov subspace recycling in combination with different preconditioners.