Pretty much any US airport that you can fly to from Ireland will have flights to Salt Lake City so it will be just one stop (assuming that SLC is where you're going to)
As jhegarty said Delta via JFK or ATL might be best since they have a hub at Salt Lake City as well so more frequent flights and you'd be on the same airline all the way (better if possible as they'll be more likely to proactively look after you if connections go wrong etc.)