Polymers are extensively employed in diverse industries, including electrical equipment and electronic devices. Recent technological advancements have intensified the demand for dielectric polymers with both high insulation resistance and high thermal conductivity. We employed molecular dynamics simulations to clarify the intricate relationship between molecular structures, thermal conductivity, and ionic mobility from an atomistic point of view. Examined polymers include polyethylene, polyvinyl alcohol, polyvinyl chloride, polyvinylidene fluoride, polytetrafluoroethylene, polychlorotrifluoroethylene, polyoxymethylene, and polyethylene oxide. Based on the elucidated correlations among force field parameters, we found that the parameters can be clustered into four groups: group 1 (atomic and bond parameters and force constant of the bond angle), group 2 (equilibrium angle and force constant of dihedral angle), and group 3 (side chain atom charges). Thermal conductivity showed relationships with parameters in group 1, with correlation coefficients mostly exceeding 0.7 in the absolute value. Considering the correlations between the parameters, we systematically altered the parameters within each group and computed thermal conductivity and ionic mobility. When altering the force field parameters of groups 1 and group 2, a trade-off relationship between thermal conductivity and ionic mobility becomes evident. Conversely, altering the force field parameters in group 3 increased thermal conductivity while decreasing ionic mobility, breaking the trade-off relationship. The proposed clustered-parameter variation method can predict the changes in the electrical and thermal conductivity of polymers through molecular structure modifications. The method, being a general and first-principles approach, is likely to have significant advantages in the molecular design across a diverse range of polymers.