NMM is not a Skyrim only mod manager - or even a Bethesda only manager - it currently can manage mods for 17 games with more to come. It is intended to be a simple manager for people who are new to modding. Mod Organizer is a very good manager, and is intended for those Bethesda games that use the same base Game engine.(including Skyrim) Because it concentrates on a specific group of games, It can do more - and is more complex as well. Comparing NMM to MO is like comparing peaches and oranges - they are both fruits, but do not taste the same. Some people prefer peaches, some oranges. Some people want simplicity, others want bells and whistles. If you are not sure, try them both there is no extra charge for that.
There are other less popular mod managers available - each with their own pros and cons. But once you decide, stick with just one mod manager.
Modding is addictive - once you add a few, you will want more - and eventually will have so many that they are conflicting - A basic rule is if two mods change the same thing in the game, they will conflict. But maybe loading one ahead of the other will allow them both to coexist (and maybe not) - then you will need a program to help sort them - the current go to for that is LOOT, NOT a mod, but a stand alone program that works with whatever mod manager you like to help keep your mods in the proper order. Get LOOT here: https://loot.github.io/
Some mods require something else to work - you find this by reading the mod description completely for each mod. The most common thing needed is SKSE ( Skyrim Script Extender) an add on program that allows mods to do things that the game maker never thought could be done.
It can be downloaded here - it is also not a mod and cannot be installed like a mod - so be sure to read the documentation.
Now, recommended mods - The Nexus keeps a running list of mods sorted by popularity for every game we support. There are multiple lists based on different criteria. The Skyrim lists are here: These will be the mods that most users recommend.