Hey there. Just chiming in with some info.
1. If you're looking to fire up Morrowind, one of the first things you'll want to do to bring it up to date is get Morrowind Graphics Extender. This program greatly enhances Morrowind's stock graphics engine. It gives Morrowind shader model 3.0 water and effects, and MGE also greatly extends Morrowind's view distance range. It comes with many other enhancement options as well. Make sure to follow the install and set-up instructions exactly as they are written. MGE can be finicky if it's not done right. This program is absolutely essential for an updated Morrowind.
2. If you want the updating process to be as simple as possible, you could grab Morrowind Overhaul which includes MGE as well as updated texture packs which will bring most of the in-game textures up to speed. This is not my preferred method mostly because I'm picky and I like things to look exactly how I want them, but if you're not super-savvy with the folder and file structures of the game and so forth, then Overhaul is the way to go.
3. Other texture packs worth looking into are ATAP and Connary's textures. Connary's are my personal favorites and some of the best textures ever made for the game. Connary has since, for whatever reason, taken his textures down from most of the major gaming sites, but the site below has a link to both of his texture packs if you're so inclined to try them out:
http://btb2.free.fr/morrowind.html
4. Better Bodies (mod). This is included with Morrowind Overhaul. If you choose not to go the Overhaul route, grab this.
5. Better Heads OR Changing faces, but not both. I personally prefer Changing faces, but both are good and will greatly increase the variety of faces you will see on NPC's in the game. I believe Better Heads is included with Overhaul.
6. Better Clothes - Also included in Overhaul. Updates the in-game clothing to fit Better Bodies.
7. Darknut's Creature Textures - Included in Overhaul. Does what you'd expect, and increases the texture quality on the in-game monsters.
8. Darknut's Weapon Textures - Included in Overhaul. Updates weapon textures.
9. Tamriel Rebuilt 1 & 2. Sure, you can play the game without these, but I (and many others) consider TR to be essential. If you're not sure what they are, these are two large mods that add the surrounding landmass around the Island of Vvardenfell (the main big island your character runs around in for most of the game). These mods together almost double the size of the landmass of the game and they are expertly and painstakingly well-made by a large group of like-minded modders, and they pay strict attention to the lore of the Morrowind universe to ensure a seamless experience. They blend in so well with the main game that you'd never know they were player-made if no one told you. Amazing mods.
10. Morrowind Code Patch - This handy little program is basically essential, especially if you have TR 1 & 2. It comes with a whole host of little bug fixes that can be independently enabled or disabled at will. It also enables the ability to increase the amount of world map that can be displayed, which you will want if you have Tamriel Rebuilt since they add so much land to the game.
11. On the Rocks! - Included in Overhaul. This is a texture replacer that covers all (or most) of the rocks in the game with much higher resolutions and gives them bump-mapping so that they reflect light realistically. If you don't go the Overhaul route, this replacer is a must.
12. Signy Signposts - This replaces the in-game scribbled signs with higher res versions complete with actual legible writing. Another must. There is a version of this mod that covers all the signs in Tamriel Rebuilt as well. Make sure to get both the vvardenfell and TR editions.
13. Vality's Grass Mod - Included in Overhaul. Adds grass to the game that sways in the wind. It works through MGE, so make sure to follow the instructions for setting it up.
14. Vality's Bitter Coast add-on - Makes Bitter Coast look amazing. It's essential in my game but taste may vary. I find it to be one of the most beautiful mods in existence.
15. Vality's Ascadian Isles add-on - Makes the Ascadian Isles region look much more dense and lush, with better resolutions for most of the plants, trees, and roads in the region. Again, essential to me, but not essential in a technical sense.
16. Animal Behavior - This makes monster behavior more realistic by making some creatures less aggressive. This mod also solves the dreaded constant Cliff Racer attacks by making it so that they don't attack you unless you attack them first. Trust me, you want this mod.
17. Windows Glow - Updates the window texture resolutions and makes them glow with candle light at night. Essential imo. It's included with Overhaul.
18. Abot's Water Life - Adds a whole slew of sea creatures such as several different kinds of fish, sharks, etc to the water and as a result the seas and lakes feel much more alive. This is an incredible mod.
19. Carnithus' Armamentarium - Adds a shop with a huge amount of very well-done armor designs to the Molag Amur region. Many of the good armor mods that have come out over the last half a decade have been based on the designs in this mod.
20. Art of War Museum - Adds a shop to the Museum of Artifacts in Mournhold that sells a large variety of very well-made weapons, armor, and tapestries.
21. Texture Fix 2.0 - There is a version of this for both the original game landmasses as well as Tamriel Rebuilt. It fixes a lot of the noticeable seams you get once you start installing updated textures as a result of Morrowind's inability to seamlessly merge more than two land textures at the same time. You will want this fix. It's included in Overhaul.
22. Nangsid's Rugs and Tapestries - Updates rugs & taps to higher resolution, with many of them being unique designs made by the author. This mod is understated, and you wouldn't think it would add so much to the game, but it does. This mod makes interiors look so much better and I couldn't imagine playing without it at this point.
Other mods worth strong consideration - Jeremey's Knight Shop, Balmora Expansion, Louis Beauty Shop, Qarl's Gothic Attire, Rideable Guars, StarWarsGuy's Better Nightsky (included in Overhaul), Better Rain, Castle Hestatur (amazing), Vurt's Grazelands Trees, Vurt's West Gash Overhaul, Vurt's Solstheim Trees, Vurt's Solstheim Groundcover, Aleanne's Clothing mods, Korana's clothing mods, Vagabond Angel's various weapon and armor mods, and many more. There are many, many good mods for this game I haven't mentioned, so I suggest taking a look at the lists of them on this site and Planet Elder Scrolls and look for things that you think might suit your own taste.
As far as the fundamental differences between Morrowind and Skyrim's gameplay:
Morrowind is considered by many to be a considerably more difficult game for people who are just beginning. Morrowind does not include quest markers or instant fast travel, though quest-givers will give you directions as to where you need to go to complete the quests. You will be hoofing it a lot, especially early on. There are modes of travel within the game in most towns and cities, such as boats and Silt Striders. Some consider Morrowind's lack of insta-travel a plus. Morrowind's landscape, creatures, and lore are so unique that you'll be so lost exploring all of it that you won't even care that you're having to run everywhere. You'll find something new and interesting around every turn.
Combat is one area where you're going to notice a difference between the games. Morrowind's combat engine is 10 years old, and it shows. This isn't a major issue for some, because you'll be doing so much other stuff besides just combat that fighting only plays a part of the whole. But it's still definitely noticeable.
However, Morrowind's character creation, armor, magic and enchantment systems are in fact deeper than Skyrim's. You can make your own spells and enchantments in Morrowind instead of having them all pre-selected for you. There are more armor slots in Morrowind, such as pauldron slots, and your weapons and armor degrade as you're hit in combat.
No one is an essential NPC in Morrowind. You can kill anybody at any time and once they're dead, they're dead. You can actually render certain quests un-doable (including the main quest) by killing certain NPC's. Be careful who you stab.
In summary, Morrowind leaves you to find almost everything out on your own. It gives you a short 5-minute tutorial on the basics and then sets you loose to do whatever. The freedom and non-linear nature of it can almost be over-whelming at first, but once you get the fundamentals down, it's ridiculously addictive (imo). The whole thing just has a certain feel to it that I've never seen duplicated in any other game. Morrowind, Oblivion, and Skyrim are all great games, but I think if you give Morrowind a chance, you'll become a fan of it. If you have any questions about how to install certain mods and you can't find the answer in the readme's or online, just post them here and I'll do what I can to answer them. Hope this info helps you. Happy hunting.