The Iliad and The Odyssey - Homer

The argument I would use to convince a sceptic to read these is the magnitude of their impact on everything that came afterwards. These are the ur-texts of western literature; essentially every educated person of the last 2500 odd years was throughly familiar with both, from Alexander sleeping with the Iliad under his pillow to yank hockey players reading the Odyssey at the last winter Olymics. Knowing these epics will bring a lot more life to other works, and not just books. If you walk into a random old building anywhere in Europe there's a good chance you will find references in sculpture or paint to episodes from Homer. Aside from that they are tremendous works in their own right (Duh! They wouldn't have survived for two and a half millennia, painstakingly and lovingly transcribed and transmitted by dozens of generations, scribes with quills twitching by candle light, monks fleeing barbarians with only time to grab a few precious items, and you don't even have the gratitude to read them!) Fagle's translations are the best modern translations in English. I have tried others. One very popular and very recent translation is not worth a moment of your time, it is so far from the spirit of the original. The Iliad comes first chronologically, but I think the Odyssey is more fun and more interesting, so probably a better place to start.