Tools to Avoid

Vortex
The mod manager was created around the idea of LOOT managing the load order, making modding seem simple and easy (see below why that's a bad idea).
While the option to manually order plugins exists, it's designed to be as unintuitive as possible - the user needs to select the position of every plugin from a dropdown menu, based on relative position to other mods (load X after Y, load X before Z), or use a graphical, node based interface.
Additionally, it does not track generated files, and the deployment logic can be confusing to the user.

Nexus Mod Manager/Fallout Mod Manager
Outdated/abandoned, have no virtual file system or even dynamic movement of mods with loose files, which can lead to complete mod, or game reinstalls in case the user wants to change the load order, or installed mods in a wrong order.

Mod Organizer 1
There is no reason to use Mod Organizer 1 over Mod Organizer 2.

LOOT
The LOOT doesn't really have any idea about your mods and their inner structure - it just orders them based on tags in a masterlist managed by volunteers, meaning that it's impossible to account for every single mod out there.
The main issue regarding LOOT in Fallout New Vegas modding is that its masterlist is heavily outdated and doesn't account for most mods added and updated in recent years, leading to completely incorrect sorting.
Incorrect load order will lead to overwriting or breaking features from mods.

Bashed Patches
These patches have their use cases and in skilled hands can save a tremendous amount of time. It's not that they should be completely avoided period.
However, like some of the other aforementioned tools, they are fully automated, and without the oversight of a human being they are liable to misidentify intentional overwrites as "conflicts" that need to be solved. For this reason, it's only recommended to use them if you are both capable and willing to comb over the resulting patch.
LOOT and Bash tags are unused by majority of the Fallout New Vegas modding community, leading to complete breakage of the automated behavior of these mods.

Mator Smash
Outdated and produces broken patches. The only viable method of automated patching available is through a properly utilized Bashed Patch thanks to its sophisticated tagging system, which allows the user to customize how the generated patch handles individual records.

zEdit/zClean
Neither have any real advantages over FNVEdit and lack some essential features due to their outdated codebase. Support is also limited.

Merge Plugins Standalone/zMerge
Automated merging can potentially cause major breakage in mods, especially heavily-scripted ones.

FallrimTools Cleaning
Cleaning save files with Resaver will only cause issues, there is nothing that needs to be done if you followed the guide properly.

Ordenador/DDSopt
Breaks many textures by needlessly converting/adding/resizing alpha channels, cubemaps and mipmaps. Use BSArch Pro instead.

New Vegas Configator
Outdated and possibly dangerous. You won't need any INI tweaks other than the ones in the guide.

Save Cleaner
Works by going through your save file and deleting every REFR file, which will most likely break your save.