Coordinating bus/train with flying into Shannon or Dublin, then on to Cork

I have searched the RS site as well as the Bus Eireann and Irish Rail sites trying to figure out what combo of bus from where to where OR train from where to where works best with arriving at Shannon airport. I want to end up in Cork. There appears to be no train from Shannon to Cork, but there is a bus from Shannon to Limerick and then a train on to Cork; there does appear to be a bus from Shannon to Cork. Does this sound correct or am I missing something? Maybe I should fly into Dublin, as there IS a train from there to Cork...Given all that, how can I determine WHICH bus or train station to use when more than one is listed in the online schedules? (Maybe I need to buy Rick's book! It's probably in there!) To keep it simple, what is the best way to get from Dublin Airport to the Dublin train station with service to Cork? Thanks, Ann. (First time to Ireland since 1972!!)