What is nice about Morrowind is that you can upgrade a lot of the graphics with mods, and you can play it on a cheap netbook (you can make a legit disc image from your disc and mount it without any problems too). That makes it nice for when you are traveling or whatever and just have your netbook.
In Morrowind, you need to do quite a bit of in-game reading to understand the plot, though.
@GuitarPerson: This above quote, specifically regarding updating the graphics with mods, is a really great way to know how to enjoy Morrowind. There will be a LOT of in-game reading, due to there being very little in the way of spoken dialogue, but it's worth it. The game will be hard to enjoy at this time because of the dated gameplay, but there is SO much in Morrowind that will make it awesome and enjoyable. The leveling system in Morrowind is what I wish was in every game, including Skyrim. Definintely play Morrowind if you get the chance, and play Oblivion as well. Most folks are recommending that you play Oblivion
then Morrowind; I would have to respectfully disagree. I recommend playing Morrowind first, get the chronological gameplay shock out of the way, then really get into Morrowind. Finish it, maybe with a few characters, including the DLC packs for it, then move on to Oblivion. With Oblivion, really, the only DLC packs I would call essential are Shivering Isles and Knights Of The Nine. Everything else is fluff. Fun fluff, but stuff that will ultimately distract you if you are simply playing through to experience the game and not to explore every possible nook and cranny and gameplay type that's available.
I say play through both of Morrowind's DLC packs because Bloodmoon has a lot of stuff in it that will give you some good background on a few references in Skyrim, and Tribunal is a great continuation of the Nerevarine's storyline after the end of the main quest in Morrowind. Also, in Tribunal, you get a chance to meet characters that you've read about in books. Whatever you do, do it for fun; if you're not really having fun, don't sweat it. Each game is designed to be stand-alone, with each previous game simply becoming more lore to flesh out the background. Fun to play through, but not necessary.