As you have a particular itinerary in mind, you should look at cards that will help lower your expenses for this trip. You'll need free flights and a free hotel stay. Below are just two suggestions off the top of my head. There may be better options out there if you do the research, but here is what I am thinking:
If you don't mind a stop over, it looks like Southwest can get you from DC to New Orleans. If you open one card and get 50,000 points, that will likely be enough to cover your flights. I believe the minimum spend is $2,000 in the first 3 months. If you travel frequently in the US and to destinations that they fly, look into getting two cards and earning a companion pass. Both my wife and I have done this and have saved $1,000s on flights. I believe it is one of the best deals going.
Hyatt has a card that gives you 2 free nights when you spend $1,000 in the first three months. If both you and your wife were to get this card, you would then have 4 free nights at the Hyatt in New Orleans. I will say that most people try to use their Hyatt free stays to stay at the higher end hotels, so you would not be getting as much bang for your buck as if you had used them to stay at a $1,000 a night property like the Park Hyatt Maldives.