Unless you are doing research on how the behaviour of these approaches differ, there is no need to use all these for model comparison. From these, LOO is the best choice. WAIC is also justified for Bayesian modeling, but the computation of WAIC fails more easily than computation of LOO, and WAIC failure is more difficult to detect than LOO failure. AIC is for maximum likelihood and no constraints. DIC is for posterior mean point estimate. Thus AIC and DIC are not ok for full Bayesian inference. BIC is assuming flat prior and can be justified only for regular models asymptotically. WBIC has even worse computational issues than WAIC. You can read more about the theory in A survey of Bayesian predictive methods for model assessment, selection and comparison and experimental results comparing LOO and WAIC in Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC.