Take the joint tests on both determining cointegration rank and the model for deterministic components by using so-called Pantula principle.
Further consult Harris, Richard “Applied time series modelling & forecasting”, Chichester : Interscience, 2002
For the bads and goods of different Information Criteria Tests, you can look it up in any Econometric textbook.
Eg. J. Johnston and J. DiNardo, “Econometric Methods”, Fourth Edition, McGraw-hill, 1997