For airlines, we have found United Airlines and Aer Lingus to be the best priced for direct flights. Aer Lingus has more flights to Shannon while United has more to Dublin, but it is ever changing so do some legwork. If you fancy a little side trip form the NY/NJ area, Play Airlines (yes, it is a real airline) flies from Stewart airport in NY (SWF) and does fly to Ireland but stops in Reykjavik Iceland. Adding a couple days to your journey there wouldn’t be horrible!
We would recommend figuring out what you want to do before/after the wedding and then figure out the airline, that may make more sense.
Merly Shattuck is a close friend and has been in the travel industry for over 10 year. Feel free to contact her about tours and travel excursions in Europe. Her email is meryl@shattucktravel.com and her website is here.