Absolutely. If the goal is “What are the oldest stories that I could actually enjoy reading?”, rather than simply the oldest surviving texts, I'd rank them roughly like this.
| # | Work | Approx. date | My take |
|---|---|---|---|
| 1 | Epic of Gilgamesh | 2100–1200 BCE | ⭐⭐⭐⭐⭐ Start here |
| 2 | Story of Sinuhe | c. 1900 BCE | ⭐⭐⭐⭐⭐ Very readable, surprisingly human |
| 3 | Atrahasis | c. 1800 BCE | ⭐⭐⭐⭐ Creation + flood story |
| 4 | Descent of Inanna | c. 1900 BCE | ⭐⭐⭐⭐ Dark underworld myth |
| 5 | Enmerkar and the Lord of Aratta | c. 2100 BCE | ⭐⭐⭐½ Heroic adventure |
| 6 | Lugalbanda | c. 2100 BCE | ⭐⭐⭐½ Adventure/hero tale |
| 7 | Enuma Elish | c. 1100 BCE | ⭐⭐⭐½ Babylonian creation epic |
| 8 | The Tale of the Shipwrecked Sailor | c. 2000 BCE | ⭐⭐⭐⭐⭐ Short Egyptian adventure |
| 9 | The Book of the Dead (selected spells/stories) | c. 1550 BCE+ | ⭐⭐⭐ Mythological, not a conventional story |
| 10 | Rigveda (selected myths) | c. 1500–1200 BCE | ⭐⭐⭐⭐ Ancient Indian mythology |
| 11 | Iliad | c. 750 BCE | ⭐⭐⭐⭐⭐ One of the greatest |
| 12 | Odyssey | c. 725 BCE | ⭐⭐⭐⭐⭐ Even more accessible |
| 13 | Mahabharata | c. 400 BCE–400 CE | ⭐⭐⭐⭐⭐ Enormous, extraordinary |
| 14 | Ramayana | c. 500–100 BCE | ⭐⭐⭐⭐⭐ Epic adventure |
| 15 | Theogony | c. 700 BCE | ⭐⭐⭐⭐ Greek gods and creation |
| 16 | Works and Days | c. 700 BCE | ⭐⭐⭐½ Myth + everyday life |
| 17 | Aesop's Fables | c. 600 BCE+ | ⭐⭐⭐⭐⭐ Tiny stories, enormously influential |
| 18 | The Histories of Herodotus | c. 440 BCE | ⭐⭐⭐⭐⭐ History mixed with wonderful stories |
| 19 | The Tale of the Eloquent Peasant | c. 1900 BCE | ⭐⭐⭐⭐ Egyptian tale about justice |
| 20 | The Descent of Ishtar (related Mesopotamian tradition) | 2nd millennium BCE | ⭐⭐⭐⭐ Underworld mythology |
If you're interested in stories as stories, I wouldn't read them strictly chronologically. I'd go:
1. Gilgamesh → 2. Sinuhe → 3. Shipwrecked Sailor → 4. Atrahasis → 5. Iliad → 6. Odyssey → 7. Greek myths → 8. Mahabharata → 9. Ramayana
That gives you a fascinating progression from Sumerian storytelling → Egyptian literature → Babylonian myth → Greek epic → Indian epic.
Gilgamesh is especially worth reading alongside the Iliad.
Gilgamesh and Achilles are separated by well over a thousand years, yet both are stories about exceptionally powerful men confronting the fact that human beings die.
Gilgamesh begins by wanting power and glory. After Enkidu dies, his whole outlook changes. He becomes obsessed with the question:
“How can I escape death?”
Achilles, meanwhile, knows that his heroic life is likely to be short. He has to choose between a long, obscure life and a short life of immortal fame.
That's one reason Gilgamesh feels astonishingly modern.
If you want just one book to buy: get a good modern translation of The Epic of Gilgamesh, preferably one that includes the complete surviving poems and some background notes.