I would suggest going for a clean install and start from scratch. Incompatible mods are quite rare among highly recommended ones, but they do sometimes require specific loading orders, this is usually in their written descriptions. As someone mentioned in a previous post, using Loot is really helpful, I always have it installed. It sorts the load order based on priority. The mods at the top of the load order are usually the ones that cause the biggest registry changes or contain several scripts that need to override existing ones. Most minor mods, including companion mods, added weapons and armor, and even slight AI adjustment (such as the one that makes NPC's hide during dragon attacks) are made without new scripts, they are instead tweaks or simple copies of ones that already exist in the game's code. They do this to avoid conflict in the load order and registry.
Most overhaul mods (whether it be skills/perks, leveling, UI, or Race mods), despite their large changes to gameplay and/or immersion, are simpler than one would think in regards to scripting, but they often require being placed higher up in the loading order. These mods are often placed directly below the main files (Skyrim and its DLC files) and any debug or patch files (which are at the top, almost in all cases). Most visual upgrades, texture packs, etc. are usually a bit farther down.
Minor mods, companion mods, weapon packs, minute AI changes, or mechanical changes (faster arrows, for instance) and presets or additions to character creation (hairstyles, beards, most of the body mods) can usually be loaded more or less anywhere without big issues. Player homes, settlement refurbishes and similar mods can usually go lower on the load list, these features became a lot less buggy with the inclusion of Hearthfire, which created a "custom" build feature that allowed the engine changes to topography and added architecture more easily.
As long as one doesn't install mods that change the same threads and features, conflicts will only arise occasionally, usually due to one or more plugins/mods being outdated. I believe Vortex has a built-in feature that not only detects whether mods are outdated but also updates them smoothly (this was not quite so smooth with the Nexus Mod Manager). Most visual mods that don't add considerable physical input, geometry, or structural changes are fine in almost any order, examples could be meshes and texture packs, as well as certain weather mods and effects.
I usually install the big mods first, the core ones. Which would be; patches and fixes - ENB and visual mods (including weather effects)- Overhaul and bigger gameplay mods (like Ordinator or Sneak Tools, Wildcat, etc.) - RacMenu and Start Another Life, plus any ragdoll or body mods - Weapon packs, armor packs, etc. (I install them before the companion mods since some companions might require certain items) - Companion mods - Minor mods such as crafting changes, character presets and hairstyles, eye packs, added spells, animations, etc. - Player Homes and similar changes, trading mods, extra guilds or factions (there are some great mods that elevate the civil war aspect of the game!).
My installation in roughly the above order is not so much about the "correct" order in regards to the actual load order of the mods, but more about making the bigger changes first so I know what kind of game I want to play. I then add in minor additions and changes to tweak this, I have about 30 companion mods, for instance, most of these were installed later on. The Nexus mods site is terrific in explaining how things work, under the requirements tab you can always see what's missing or what other mods or parts might be required in order to make any mod work. So long as the main game is up to date and the most important patches are installed and you stick to the more streamlined, endorsed mods, you should be fine. The most common issue for me was clipping issues on certain companions, which was often caused by lacking items or conflicts with other companion mods or body mods. Certain large-scale player homes crashed me to desktop (there were two notorious ones, but I can't recall their names right now), this turned out to be a Hearthfire issue where the mods had simply overwritten certain commands set by the engine without providing a stable alternative (in other words; they were poorly made).
Get this bad boy to help with the load order! https://loot.github.io/
Should you run into issues and need a quick but helpful checklist on load orders in general, this one is very good and easy to follow:
https://skyrimseblog.wordpress.com/load-order-structure/
As for the video you linked; most of the issues associated with Bethesda's main files are cleaned via unofficial patches and fixes, as well as official updates to the core game itself (there was quite recently a 500-600MB update to Skyrim SE). I never did anything like that, and the game is probably more stable now than when I last played it properly.
PS: Immersion mods are your friends, they, in conjunction with atmospheric mods and visual upgrades, create a brand new game experience. Along with improved combat, stealth, and a slew of deepened mechanics, it becomes a completely different game. When I made the plunge into mods and did my third playthrough, I simply got stuck in a place where I can't even imagine playing vanilla Skyrim again. And we haven't even mentioned content mods, there are some that add entire DLC-sized maps and content. Have fun!