Continental, Jet Blue or Delta. They all have direct flights so you be on the plane for less amount of time. All are safe. I would just suggest looking at
for the best deal during the time you are going
I suggest any one of the older more prominant and better known airlines such as Delta, Continental or Northwest if those carriers fly that route. I also would suggest AirTran if available. I have found them to be a quality airline and their fares are usually pretty much in line with all the others if not less than most others. I would stay away from Southwest because even though I have flown them many times and have been happy, the latest news is negative about them saying they have had several planes grounded for safety/maintenance violations ..... kinda scary. Also I have had more than one terrible experience with Spirit and I refuse to fly Spirit again regardless of ticket price. I consider Jetblue and Virgin airways second rate to some others.
A non-stop flight is almost always better than having to change planes. From New Orleans (MSY), Jet Blue flies non-stop to JFK, Continental flies non-stop to Newark (EWR), and American flies non-stop to La Guardia (LGA).
Check the travel sites (like Expedia & Priceline) and also the airline sites for the best deals & schedules. I believe you have to buy JetBlue tickets directly from them as they don't sell via the travel sites.
there is a kind of metasearch called http://mobissimo.com
you can check http://blog.lessno.com - there from time to time they publish info on rates and good deals (they sell tickets too)
JetBlue Airlines because they have comfortable planes, and personal televisions with DirecTV.