Time Series modeling --criteria

Give criteria for aiding in the choice of a “best” time series model when two or more such models are available. What is, arguably, the most important criterion?

I think that for the above, isn't the AIC, BIC the most arguable? I would look at autocorrelation plots, but I am trying to see what is missing in this and how to handle on the multiple models. Please elaborate with details, and thanks