Questions about train travel from Dublin to Ennis

You buy one ticket from Irish Rail, departing from Heuston Station and change at Limerick (usually). Make your selection carefully and buy the advance fare (€16 vs €30) now. https://www.irishrail.ie/en-ie/
If you are traveling to Ennis directly from the airport, most folks advise taking the bus, rather than going into the city to get the train. https://www.dublinairport.com/to-from-the-airport/by-bus

The difficulty is that you don't know what time your flight will actually land, so don't know for certainly what train or bus you can make.
A ticket bought on the day at the station costs 45.50 Euro. The cheapest web fare is 15.99, but only changeable until 48 hours before travel, then 18.99, changeable until 24 hours before, or 29.50 changeable until 1 hour before.
The first two are no use to you, and with the 3rd you could still be in the air with no internet access, in a worst case.
So the 45 Euro option is the sensible one.
You may find when you land and have data or Wi-Fi that there is still one of the cheaper quota controlled web fares available.
Sometimes you take a Galway train and change at Athenry, sometimes a Cork train and change at Limerick Junction. To Heuston you take Dublin Express bus #782 every 20 minutes.
The direct bus City link #712 leaves the airport at 0600, 0800, 1200, 1600, 2000 and 0030 , so you could have a very long wait in which time you could have been on a train.