Coarse-grained (CG) models allow for simulating the necessary time and length scales relevant to polymers. However, developing realistic force fields at the CG level is still a challenge because there is no guarantee that the CG model reproduces all the properties of the atomistic model. A recent promising method was proposed for small molecules using statistical trajectory matching. Here, we extend this method to the case of polymeric systems. As the quality of the final model crucially depends on the model design, we study and discuss the effect of the modeling choices on the structure and dynamics of bulk polymers before a quantitative comparison is made between CG methods on different properties and polymers.