Well, last summer I flew Seattle - Dublin - Edinburgh on Aer Lingus in buisness class. Highly recommended. A wonderful flight across the pond - Aer Lingus business class is great. The last leg (between Dublin & Edinburgh) is on a turboprop, so no fancy seats there, but it's a short hop (on technically on Aer Lingus' regional partner called Stobart Air), flight is less than an hour, so a non-issue.
Dublin is a fairly easy airport to connect through. Be patient though if you check a bag and need to cliam it, baggage claim in DUB was slow and a bit confused.
If you're on Aer Lingus in business class, you'll get to use their very nice lounge in DUB. There's also a Chocolate Cafe restaurant in the terminal outside security (available to anyone) which was a nice touch (lots of chocolate treats, but they also serve other dishes, so you don't have to go completely into sugar shock).
I'll add that I found the airport in Edinburgh to be a bit of a cluster...one of the worst, most disorganized and chaotic security check systems (TSA equivalent) I've ever experienced in a developed country - what a mess! That was during peak summer season, but it was shockingly bad.
If you go on Aer Lingus in business, try for one of the "throne seats" (aka "Captain Kirk" seats), you get a crazy amount of room and not one but two large tables on each side of your seat to spread out your stuff. Great service and decent food, a very nice way to fly to Europe. Tastes vary, but I've flown both Delta and United's business class on flights to/from Europe in the past 2 years and both were nice, but I prefer Aer Lingus.
If I were coming from New Orleans, on Aer Lingus, I'd connect through Chicago rather than any east coast hub. For me, one of the major reasons to go business class is to get some solid sleep on the plane and arrive happy. Flights to Ireland from the east coast are too short to get a good nights sleep, so I always try to maximizing the trans-atlantic leg. Starting that flight from Chicago gets you one more hour of sleep on the plane (of course, it depends to some extent on the details of getting to Chicago and your layover there...then again, I try to avoid east coast airports like the plague for other reasons).
Good luck and have fun!