The rheological properties of a dilute solution of polymers in a good solvent are predicted by incorporating excluded volume effects and hydrodynamic interactions into a Hookean dumbbell model. We use a narrow Gaussian repulsive potential between the beads of the dumbbell to model the effect of excluded volume. The linear viscoelastic relaxation modulus is estimated using Brownian dynamics simulations and a Green-Kubo relation. When excluded volume interactions dominate, a stretched-exponential function is shown to better describe the decay of the relaxation modulus with time, than a simple exponential decay. Although the excluded volume and hydrodynamic interactions are nonlinear phenomena, Brownian dynamics simulations show that their influence on viscosity and first normal stress difference coefficient is approximately additive. This linear coupling, however, is not true for the second normal stress difference coefficient. Results of Brownian dynamics simulations also show enhanced shear thinning as the solvent quality improves. The results of the simulations are compared with predictions obtained by assuming that the configurational distribution function is Gaussian. The Gaussian approximation is accurate in certain ranges of the model parameters and in overall qualitative agreement with the Brownian dynamics simulations.