As above I would recommend a Visitor Leap card.
Thee are separate rail, luas and bus tickets but the Leap card and particularly in your case the 3-day (actually 72 hours from first validation) Visitor Leap at €19.50 would be by far the best value and validity.
Before Leap there was a more extensive range but similar to London Travelcards they purposely reduced them and made them more expensive to encourage Leap card use.
As well as Dublin Airport the Visitor Leap card can be bought in the City centre at the Dublin Bus office in O'Connell Street and tourist offices. At Heuston station as well as Busaras, which is the bus station for national and regional routes located a short walk from Connolly station. In both of these it is not from the ticket desks but Easons which is a newsagent chain.
Visitor Leap can also be bought online and posted to you, assuming your trip is far enough away for postal times, they just use regular non-tracked post for this.
https://about.leapcard.ie/leap-visitor-card
Although I would recommend Visitor Leap for your apparent use a regular PAYG leap can also be used, it's daily cap for Dublin bus, tram and train is €10 or €40 for a week. There is also a €5 deposit for the card.
The Rail only cap is €9.50, bus only or tram only is €7.00 so not much to be saved by sticking to one mode for a day, especially as the Rail and Tram networks are quite small.
Similar to Oyster and other such systems there is a max journey time for PAYG on Leap so if you are travelling around without leaving the rail or Luas by tapping out and in for extended periods you may break this and get incomplete journeys. Visitor Leap doesn't have this issue.
For rail use you tap in/out at barriers or validators at stations without barriers, luas the same, tap in/out at validators. It is necessary to do this with regular Leap, Visitor Leap doesn't need to be tapped at all as once the day/72h pass is activated it is valid for the duration but you will need to at barriers.
For bus use there are 2 validators, one on the driver's ticket machine and one on the right opposite the driver's cab. Visitor leap should be validated on the right hand validator. Regular leap will work on both but the right hand validator deducts the full fare for the route while using the driver's validator as well as stating your destination is necessary to get short-distance fares.