This is a list of some of the quest mods I have played, and sorts them by suggested player level, and whether they are suitable for non-dragonborn characters (if you have not started the main quest yet, or are role-playing a non-dragonborn).
The suggested level mainly depends on the combat difficulty of the mod, but also considers the story and how powerful the loot is.
Also, within each level category, quest mods are loosely sorted by how good they are - starting with the "best" mods and ending with "average" mods.
I will occasionally update this list as I play through more quest mods.

Non-dragonborn lvl 10+
Interesting NPCs - misc. quests
Identity Crisis
The Cheese of Ages
Primeval Real Estate
A Feathered Friend
Fortune's Tradehouse
EasierRider's Dungeon Pack
Ogmund's Tomb

Non-dragonborn lvl 20+
Beyond Skyrim Bruma (has some hard speech skill-checks)
Interesting NPCs - full quests
Interesting NPCs - The Aldmeri Prisoner mini-questline
Interesting NPCs - Darkened Steel questline
Carved Brink
The Tale of Tsatampra Xiros
The Secrets of Arc Cyrae
The McMiller Chronicles
Temple of Phynaster
Curse of the Hound Amulet
Middle Earth Redone

Non-dragonborn lvl 30+
Clockwork Castle
The Forgotten City
The Shire
Away - Come Away
Helgen Reborn
Undeath
The Evil Mansion
Conan Hyborian Age
Idemdall's Folly
Path of the Revenant
Agent of Righteous Might

Non-dragonborn lvl 50+
Beyond Reach
Falskaar
Project AHO
Dwemer Colosseum
Teldryn Serious
Hammet's Dungeon Packs (most of the dungeons in this pack)
Gothic Orpheus Project

Non-dragonborn lvl 70+
Darkend (has dragons, but they don't trigger soul absorption when killed)
Immersive Idiots (starts easy but gets very hard later on)
Jurgholm
Hammet's Dungeon Packs (a few of the harder dungeons in this pack)
Sword of Sigdan

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Dragonborn lvl 10+
Interesting NPCs - Blood of Kings questline
The Island
Insanity Clause

Dragonborn lvl 20+
Yellow King
Moonpath to Elsweyr
Orange Moon
Red Flame

Dragonborn lvl 30+
Wyrmstooth
Moon and Star
Konahrik's Accoutrements
The Tools of kagrenac
Mirai
Song of Parkin-san

Dragonborn lvl 50+
Voyage to the Dreamborne Isles
Rigmor of Bruma (story is designed for new characters, but combat is very hard)
M'rissi's tails of troubles
The Hanging Gardens (has a random dragon encounter)
Vominheim
Glamoril
Fight Against the Thalmor

Dragonborn lvl 70+
Unslaad
Death Consumes All
Dwemertech