igooseman: Bugfixes and Essentials:
- Fallout 4 Script Extender (F4SE) (https://f4se.silverlock.org/)
- Address Library for F4SE Plugins (https://www.nexusmods.com/fallout4/mods/47327)
- Buffout 4 (https://www.nexusmods.com/fallout4/mods/47359)
- Baka ScrapHeap - Script Memory Limit Expander (https://www.nexusmods.com/fallout4/mods/46340)
- High FPS Physics Fix (High FPS Physics Fix) (https://www.nexusmods.com/fallout4/mods/44798)
- Rusty Face Fix (https://www.nexusmods.com/fallout4/mods/31028)
- Shadow Boost FO4 (https://www.nexusmods.com/fallout4/mods/63482)
- Interior NavCut Fix (https://www.nexusmods.com/fallout4/mods/72904)
- Unofficial Fallout 4 Patch (https://www.nexusmods.com/fallout4/mods/4598)

Only for RTX-GPUs with enabled weapon debris
- Weapon Debris Crash Fix (https://www.nexusmods.com/fallout4/mods/48078)

Must Haves:
- Mod Configuration Menu (https://www.nexusmods.com/fallout4/mods/21497)
- Extended Dialogue Interface (https://www.nexusmods.com/fallout4/mods/27216)
- Backpacks of the Commonwealth (https://www.nexusmods.com/fallout4/mods/29447)
- Automatically Lowered Weapons (https://www.nexusmods.com/fallout4/mods/20093)
- Laser weapons 1st person reposition (https://www.nexusmods.com/fallout4/mods/23102)
- Fill'em Up Again (https://www.nexusmods.com/fallout4/mods/12674)
- Crafting Highlight Fix (https://www.nexusmods.com/fallout4/mods/27479)
- QuickTrade Redux (https://www.nexusmods.com/fallout4/mods/41101)
- New Equipment Overhaul (NEO) (https://www.nexusmods.com/fallout4/mods/65761)
- Remove Weapon Mods (https://www.nexusmods.com/fallout4/mods/10267)
- See Through Scopes (https://www.nexusmods.com/fallout4/mods/9476)
- Professional Ammo Crafting (P.A.C) (https://www.nexusmods.com/fallout4/mods/22175)
- No more floating razorgrain (https://www.nexusmods.com/fallout4/mods/13823)
(not really essential; but my OCD kicks in everytime I see them floating)

Quality of Life:
- Faster Terminal Displays (https://www.nexusmods.com/fallout4/mods/937)
- Power Armor Fast Exit and Enter (https://www.nexusmods.com/fallout4/mods/586)
- Simple Wait Anywhere (Lightweight) (https://www.nexusmods.com/fallout4/mods/55597)
- Sofa Surfer - Sleeping on Couches (https://www.nexusmods.com/fallout4/mods/24944)

It's cheating; but if you have enough of the lockpicking and hacking-minigames
- Easy Lockpicking and Hacking (https://www.nexusmods.com/fallout4/mods/31527)

Audio
- Project Reality Footsteps FO4 (https://www.nexusmods.com/fallout4/mods/35904)
- Reverb and Ambiance Overhaul (https://www.nexusmods.com/fallout4/mods/10189)

Settlement
- Place Everywhere (https://www.nexusmods.com/fallout4/mods/9424)
- Faster Workshop (Workshop Lag Fix) (https://www.nexusmods.com/fallout4/mods/35382)
- Longer Power Lines (https://www.nexusmods.com/fallout4/mods/2241)
- Settlement Attack Spawns Outside the Settlement (https://www.nexusmods.com/fallout4/mods/57685)
- Settlement Repair Bot (https://www.nexusmods.com/fallout4/mods/37933)

You should be carefull with "Scrap Everything". You can literally scrap everything (even roads etc.).
In some cases it can cause serious issues with pre-combines. If you just want a cleaner settlement use
- Clean My Settlement REDUX (https://www.nexusmods.com/fallout4/mods/58757)

HUD
- FallUI - HUD (https://www.nexusmods.com/fallout4/mods/51813)
- FallUI - Inventory (https://www.nexusmods.com/fallout4/mods/48758)
- FallUI - Icon Library (https://www.nexusmods.com/fallout4/mods/60579)
- FallUI - Map (https://www.nexusmods.com/fallout4/mods/49920)
- FallUI - Workbench (https://www.nexusmods.com/fallout4/mods/49300)
- FIS - The NEW FallUI Item Sorter (https://www.nexusmods.com/fallout4/mods/60580)

If you have a Ultrawide-Monitor
- Ultra Wide Interface (21x9) (https://www.nexusmods.com/fallout4/mods/65677)

These mods should be safe to use and a good base to add mods on top of it.

Great Mods, but they overhaul the gameplay (I don't know far you want to mod your game)
- Sim Settlements 2 (https://www.nexusmods.com/fallout4/mods/47976)
- Everyone's Best Friend (https://www.nexusmods.com/fallout4/mods/13459)
- Better Locational Damage (https://www.nexusmods.com/fallout4/mods/3815)
- Better Explosives (https://www.nexusmods.com/fallout4/mods/3648)
- Better Power Armor - Redux (https://www.nexusmods.com/fallout4/mods/61146)
- Better Companions (https://www.nexusmods.com/fallout4/mods/18547)
- We Are The Minutemen (https://www.nexusmods.com/fallout4/mods/6443)

If you play in Survival Mode
- Unlimited Survival Mode - F4SE (https://www.nexusmods.com/fallout4/mods/26163)

Update:

Suggestion for Fallout 4 safe-modding:
- Don't mess with pre-combines!
(leads to FPS-Drops, flickering and sometimes whole buildings can disapear and you can fall through the floor)
- Don't remove script-heavy mods/overhauls mid playthrough!
- Use a Mod Manager! Vortex is fine for beginners and it has a "build in auto-mod-sorting-feature".
- Take a minute and read the descriptions (for conflicts with other mods and as an excuse to drink more coffee).
- Look out for Compatibility-Patches (in case of known conflicts).
- Use LOOT in addition to your Mod Manager (LOOT have more usefull tips like if a mod needs addtional cleanning)
- Use FO4Edit (for cleaning/editing mods and to create a "Merge-Patch")
- Use Wrye Bash (to create a BASHED-Patch for leveled list)

Tools for Fallout 4
- LOOT (https://loot.github.io/)
- Fallout 4 Configuration Tool (https://www.nexusmods.com/fallout4/mods/102)
- FO4Edit (https://www.nexusmods.com/fallout4/mods/2737/)
- Wrye Bash (https://www.nexusmods.com/fallout4/mods/20032)
- Optional: FallrimTools - Script cleaning and more (https://www.nexusmods.com/fallout4/mods/22633)

Video-Tutorials
How to Clean Mods & DLC
https://www.youtube.com/watch?v=YpRinGULJGw

The BEST way to create a MERGE PATCH
https://www.youtube.com/watch?v=x0kEWbGnYik

How to use FallRim Tools (Optional for "cleaner" save-files after removing mods)
https://www.youtube.com/watch?v=hyPDQuWg6jQ

NowhereDan27: What do I need to do to install mods in this version since the Mods menu is disabled in-game? Just put them in the Data folder?

igooseman: You can use Vortex (https://www.nexusmods.com/about/vortex) or Mod Organizer 2 (https://www.nexusmods.com/skyrimspecialedition/mods/6194).

Vortex is beginner-fiendly and gets everything done and MO2 ist mighty; but some induction is necessary.

Video-Tutorials
Vortex
https://youtube.com/playlist?list=PLE7DlYarj-DfYgxma5znKGYEqAHDU_WU-

Mod Organizer 2
https://www.youtube.com/watch?v=4DEzehXK1TA
https://www.youtube.com/watch?v=Ksp_yPq637s
https://www.youtube.com/watch?v=mqjzxQ7D-ZQ
https://www.youtube.com/watch?v=qOCAo5RTgso
https://www.youtube.com/watch?v=utNBS4LflIc

igooseman: https://youtube.com/playlist?list=PLE7DlYarj-DfYgxma5znKGYEqAHDU_WU-

Sync108: The dash "-" needs to be inside the url tag.

Sync108: Is it possible to manage both FO4 Steam and FO4 Steam versions in Vortex?

Sync108: Is it possible to manage both FO4 GoG and FO4 Steam versions in Vortex?

csanjuro: what mods are essentially for the best FO4 experience?

igooseman: It should be possible with MO2.
I'm not sure about Vortex (I never tried it).

Bibbsi: I am happy that "Fallout 4" is finally available on GOG. As with Skyrim, I've been waiting a long time to finally be able to play without Steam. But I think with the Creation Kit it will be again nothing (what I find a real pity). Well, i will see.