Hi Pete, I would certainly encourage you to experience a Mardi Gras at least once in your lifetime as it is like nothing else you'll ever experience; however, you need to figure out what type of MG you really want to experience.
First off get familiar with New Orleans wonderful tourist guide, nola.com as there is a MG 101 for first timers located on the site.
I'll let you in on one of my experiences. I am a lifelong resident of Southeast LA and have been to all of the parades most of the years of my life (I also marched in them for many years as well) so I am used to MG and have experienced it in every community in and around New Orleans. My dad decided when I was 15 (almost 16) to take me and my boyfriend to the french quarter (FQ) to experence how different the atmosphere was there from what if would normally be on the parade route a few blocks away. As usually we woke up at 4 am so that we could locate a parking space in the FQ (we parked here at 5:30 am). The FQ was already up as the first site I saw after exiting my dad's car was a 45+ yr old man walking around with a tie, knee socks with the garder to hold them at knee level, shoes and a brief case and yes he forgot to wear his clothes. I saw this man both in the a.m. and then again around 4 p.m. after seeing many other naked people throughout the day. I also got to experience many hilarious people in silly costumes, begging for beads, drunks, people peeing in the streets, people fighting and being arrested for public drunkeness/brawling and many people vomiting. As the day progressed and the FQ became overwhelmed with the people who walked in after the parades ended and the streets became jammed to capacity where you couldn't walk anymore then I personally got gropped and several people realized that they had been pickpocketed. There is everything attached to MG, both good and bad, and this is where you have to be able to make sane decisions by not getting drunk or taken advantage of.
MG day is 2/5/2008 (fat tuesday). That weekend is a straight 5 day party in the FQ (24/7 it doesn't stop). Prior to hurricane katrina most of the name hotels (hilton, holiday inn, hamptons, marriot, sheraton, etc) would only sell you packages for that weekend (meaning you had to spend 3 to 5 nights at the very least). Hotels would be booked before xmas for the MG season. I recall the 2007 MG had recovered to where the hotels had reported being 85 to 90% booked so I do not know if they will still make you buy a longer package. Generally our MG attracts over a million people to them so at various points the FQ will be filled to capacity and the party will be in full session.
What a lot of people don't realize is that MG last several weeks for the people in and around N.O. If you are looking for a good time and want to experiece a few parades and wonder into the FQ without 250,000 people jammed in (such as on the weekend upto fat tuesday) then I would tell you to come in the last weekend in January (23,24, 25) and their will still be parades, fewer people in the fq but you will still find the naked show going on and most of the hotels shouldn't require you to purchase a longer package for the first weekend of MG.
If you decide that you definately want to experience the 2nd weekend of MG then I would tell you to go all out. MG history explains that MG started as a way to introduce debutauntes into society so each MG parade either has a ball or extravaganza. I would tell you to look into purchasing tickets to Endemion, Bacchus or Orpheus' balls as it is a wonderful way to experience MG without having to stand in the crowds. Be aware that the average ticket to get you into one of these balls ranges from $130 to $150 per person and requires formal dress (tux's and ball gowns). Each ball differs as to what you can bring in (alcohol/food) or if you'll be offered some of this while in the ball (can purchase alcohol while at the party). The Endemion extravaganza is really wonderful as it is held in the Superdome, the party begins a couple of hours before the parade winds it way to end in the dome so you get a close up view of all the floats and bands and all the throws (watch out as you can get really hit hard by the beads - I have seen people bleeding at these things). After the parade passes through then the live bands come out, the revelers off the floats come in to great their families and guest and everybody begins to dance (there will be at least 2 big acts such as Kasey and the Sunshine Band and you'll dance your booty off). These parties end in the a.m. and most of these people wind their way in the FQ to await the morning sun. It is an experience.
Do your research on nola.com and just don't choose to wing through most of Mardi Gras because you will miss a lot of what can be experienced. Hope I have been helpful.