The role of specific and non-specific interactions in the receptor-mediated endocytosis of nanoparticles is analyzed. The characteristic time tau(w), the threshold R(th) and optimal R(opt) radii for particle endocytosis are estimated as a function of the binding energy factor C, bond elasticity factor G, and non-specific attractive/repulsive factor F at the cell-particle interface. It is shown that the contribution of F is as important as that of C and G. General and ready to use formulas are presented that can be a guide in designing nanoparticles with controlled endocytic performances.