Okay, so The Epic of Gilgamesh is a 3000-year-old poem from a culture you know practically nothing about, featuring weird characters and gods you've never heard of, and is preserved on clay tablets that are broken in many places, resulting in weird gaps in the text. Sounds pretty challenging, doesn't it?
Not as much as you might think.
The last thing this poem wants to do is bog you down with lots of details about an ancient society. The story itself is a classic adventure tale, full of fights, love, chases, and close brushes with danger with vivid characters, whose emotions and interests seem barely different from those of people today. Even when these characters get complicated (as when Gilgamesh can't decide if he's mourning for his friend or for his own mortality), it's pretty much always going to be in ways you can relate to from your own experience.
As for that whole being recorded on broken fragments bit, depending on which translation you're using, this actually might not be a problem at all. In his Gilgamesh, Stephen Mitchell uses his imagination to fill in all the broken bits, producing a smooth, readable text that sounds like it was written yesterday. Even though some other translators use brackets, question marks, and dots to show readers which parts of the text are actually missing, trust us: their translations are still a lot easier to read than your last text message.
So toss that phone aside, and give Gilgamesh a go. This epic's at base camp, baby!