You'll save money, and you'll be indoctrinated into the concept of being packed like a sardine - better get used to it. The links below represent companies we've had good experiences with and fully endorse. Give yourself plenty of time to drive or to check through airports and rail terminals. Generally, I recommend against driving to Mardi Gras. This is because the parade routes and the crowd congestion in the Quarter make it nearly impossible to drive.
Cruises are lots of fun, and a number of the major cruise lines serve New Orleans.
Some cruises originate in New Orleans, while other make New Orleans a port of call. Obviously, you will need to be sure your ship is scheduled to be in New Orleans on Fat Tuesday. You will enjoy a huge Mardi Gras party from your boarding point all the way down to New Orleans. There are contests, plenty of Cajun food, a live band, an extra lounge car, and enough alcohol to float a battleship. Mardi Gras Man will be catching the March 3rd train in Memphis on the morning of the 4th.