Background on me: Experience cruiser with over 20 cruises on a variety of lines and I have never been on a bad cruise. I am male, 50, traveling with spouse and two boys ages 14 and 12.
We have sailed out of New Orleans many times (we live in NO) and find the best time to get to the port is about 11:00 AM. This year we arrived about 11:20 and were in the Windjammer by 12. Also if you are a past cruiser register with the Crown and Anchor program by RC, there is another line for C&A members and it is much shorter than general boarding. My brother arrived at the Port about 1:00 and it took him over two hours to get on the ship.
Alcohol tip here, if you want to bring extra wine on the ship. Just put two bottles in your carry on, but have your spouse go through another security line with another two bottles in their carry on. We got four bottles of wine on board, but could have brought much more, no one pays any attention in security to who is with who, just don't put more than two bottles in each bag. Also, we brought two case of water on board that we checked at the pier and both made it to our cabins. I met someone on board who paid $88 for the "water package" this seems pretty high to me for water. Also did not buy the new drink package as it is just way to expensive considering all adults in one cabin have to purchase this package.