In my opinion, a player's first time through the game should be "vanilla". If you don't know and understand what's there and why it was done that way, you can't make a rational decision as to what to change without making unforseen changes that can have a negative effect on your experience.
I still avoid mods that alter the "feel" of the game. Some things, like graphics enhancers, can alter the overall "look", and I try to stick with those that stray the least from that original concept. I use Visual Packs (along with VP XT and VP Nature) as a "base" replacer, but with a LOT of textures from many other texture sets overwriting selected elements of those. Better Bodies, with an even higher resolution texture replacer for that, gets rid of the "puppets on strings" look of the vanilla bodies, and does a lot to make the NPCs look less like cartoon characters, without straying from the intent of the original artwork.
Changes in gameplay, such as GCD or MADD Leveler, or the MPP and MCP, get rid of what I consider "annoyances", and correct things about the original "vanilla" game that don't mesh with the world and the way I perceive it. I add them to "fix" immersion, rather than to break it.
I often use NoM to add food and sleep requirements to the game, Morrowind Crafting (or else Complete Morrowind on rare occasions) to play a "survivalist" or "tradesman" type of character, and generally some version of MCA to make the towns and cities a little less deserted (I'm not overly fond of the more radical departures from the original game in the 5.x versions). The Tamriel Rebuilt Project's mainland expansions add huge addtional areas to the game, while remaining very faithful to the original "feel". These types of mods work "in addition to" the original gameplay elements, not "instead of".
Mods like "Rich Creeper" or "MCA 5.x", that ether alter existing elements in drastic ways or add things that don't fit the original look and feel, are what I consider either "cheats" or "difficulty enhancers". Some players like them for what they want out of the game, but I find that they alter the balance far too much for my tastes. I generally avoid those, although there are days where it's amusing to load up some game-breaking mod and just do something off-the-wall because you feel like it, then remove the mod and delete the character.