There are various Skyrim modding tools that are very useful and will help users with problems they encounter during game play.  From investigation and solving to passing along helpful information to other modders or mod authors, these tools are not necessary for the game to function, but their utility and lack of impact on game/system resources means there is no reason not to install them.  These are broken into two classes: basic and more advanced.  The advanced tool users should have the basic utilities loaded as well.

Base Recommendations
SKSE - adds extra scripting capabilities and is used by quite a few mods.  Very robust in spite of it's alpha nomenclature.
Address Library for SKSE Plugins - makes SKSE mods that have been properly coded agnostic to the version of SkyrimSE.exe.
Engine Fixes - a number of extremely useful tweaks that greatly improve the functioning of the game.  For large load orders, it is essential.
Papyrus Tweaks NG - similar to Engine fixes, a number of improvements to the Papyrus scripting engine.  Set 'bSpeedUpNativeCalls = true' for a significant speed boost when executing multiple papyrus functions.
NPC AI Process Position Fix - NG - fixes a Skyrim engine limitation where it could only update an NPC’s AI process position for one hour at most if that NPC is loaded in current loaded cells.
Bug Fixes - another mod containing fixes for Skyrim's engine.  Safe to use with SSE Engine fixes.
powerofthree's Tweaks - Collection of engine bug fixes and tweaks. SKSE plugin.
.NetScriptFramework - crash logging tool for 1.5.X versions of SkyrimSE.exe.
Crash Logger SSE AE VR - crash logging tool for 1.6.X versions of SkyrimSE.exe.
Mannequin Management - system for keeping mannequins in place.
CoMap - allows adding custom map/compass marker designs.
More Informative Console - advanced informational tool that works with the console.
Equip Enchantment Fix - Fixes engine bugs where item enchantments don't apply when equipped or stop working while the item is still equipped.

Note: these two items together are suggested for people running v6 who use TCC but would like something similar to craftloot. It will not be quite the same, and you will need to refer to Kriana's instructions for the second mod to insure it works correctly, but it will provide similar functionality.

Crafting Pulls Resources From Containers - Crafting Stations scan for nearby 800 units of containers accessible for player.
Legacy of the Dragonborn config for Crafting Pulls Resources from Containers - A shortcut to help you configure Crafting Pulls Resources from Containers to work with Legacy's Safehouse crafting storage.


Advanced Recommendations
Craftloot, Sort and Storage Patches - adds items from mods to the craftloot, sorting, stash spell and storage system from the start.
Formlist Manipulator - add forms to formlists at game startup to reduce the number of conflicts between mods.
Powerofthree's Papyrus Script Extender - extends Papyrus script functionality, with over 275 new Papyrus functions, and 29 events.
PapyrusUtil SSE - adds several new scripts that provide various conveniences related to data storage and other misc functions for the scripter/modder.