The article addresses the computational efficiency and implementation simplicity of higher-order inelastic virtual elements. Compared to standard FEM, VEM lacks the simplicity of formula derivation and computer implementation. This issue becomes particularly significant as the number of polygons or polyhedral corner points increases, the order of the VEM increases and especially for 3D problems. When applied to nonlinear, path-dependent, coupled problems such as finite strain plasticity, computational efficiency in evaluating the element tangent matrix and residual decreases considerably. The paper demonstrates that final efficiency strongly depends on considering the sparsity structure of the integration point matrices in the projection equations, consistency part integration, and stabilisation part integration. The sparsity structure of integration point matrices is examined for energy stabilisation, DOFI stabilisation, and stabilisation-free formulations. A fast quadrature compression method based on computing discrete Leja points via LU factorisation is also discussed, which, for a given accuracy, reduces the high number of integration points resulting from decomposing an arbitrary polyhedron into a union of tetrahedra. The introduction of Leja points offers many advantages to inelastic VEM formulations that standard FEM-based inelastic formulations do not provide. For example, the VEM mesh can be remeshed while the integration points remain at fixed spatial locations. The advantages and disadvantages of different formulations are discussed using characteristic examples.