1. Many old and obsolete mods on nexusmods.com. Check the upload date, and the latest update, and see if there are any bug reports. Also helps to glance through the comments.
2. The mod with the most endorsements isn't always the best. Some of those endorsements are years old. Check out what's popular and what's trending.
3. Always read the requirements and note any reported conflicts.
4. There is a limit of 255 mods, but you probably won't have anything close the first time, so don't worry too much about it.
5. Be wary of mods that may conflict with something you already have. A looks enhancer may conflict with a different one, or clothing that is designed for a different body. A Diamond City revision may conflict with another mod that changes the same area. When in doubt, leave it out.
6. Some caution in adding new homes and settlements. Once you have added a mod with a workshop, you can't remove it without ruining all your saves. You're just stuck with it. So choose wisely.
Some very basic mods that I would recommend (everyone here has a different list):
Caliente's Beautiful Bodies -- requirement for MANY looks enhancers and clothing mods
BodySlide and Outfit Studio -- also a common requirement
Looks Menu -- Likewise
Weaponsmith -- adds a good variety of craftable weapons
Armorsmith -- same for armor
Homemaker -- lots more things to craft in your settlements
Wearable Backpacks and Pouches -- makes it easier to lug the loot around
Better Settlers -- adds 240 new settlers
Unofficial Fallout 4 Patch -- really essential
Fallout 4 Script Extender -- essential
Armor and Weapons Keywords -- essential
Expansions that make your game richer and more interesting:
Tales from the Commonweath
Outcasts and Remnants
Fusion City Rising
General utilities that aren't essential, but make the game easier and more fun to play:
Longer Power Lines
If you are a beginner, you may find Vortex easier to use than the Mod Organizer. The Nexus Mod Manager is no longer supported, so I wouldn't recommend that.