Aer Lingus had the cheapest fares to Ireland when we went there last year, but the "cheap" fares you see advertised only apply if you're flying directly from one of the hubs like L.A., Chicago, or Newark. If you need a connecting flight from other cities, the price goes up pretty quickly--but this applies to other airlines as well.
As for the US immigration checks at the Dublin airport, that means you clear US customs at the point of departure so when you arrive at the first stop in the US, you don't have to go through the customs lines upon arrival -- just pick up your bags and walk out the door or to your connecting flight. I think, but am not sure, that they do that at the Shannon airport as well. Also, if I recall correctly, it may only apply to US citizens, so if you're traveling on other than a US passport, you can't do the shortcut at Dublin (or Shannon) and must go through customs when you land in the US.