The content of Homer's epic poems are as straight forward as LOTR, at least. The "ancient Greek in hexameter verse" part is difficult but you can read a solid English prose translation like any person that's in it for the story. Homer is way more interesting than LOTR but not because of its philosophical complexities or anything like that.
Here's the thing with those epic poems, their content is not difficult, it's the way the story is told that many people can't stomach. Basically those old stories have no sense of suspense at all. For example when we finally see Odysseus coming back home and seeing his family for the first time, everything on the narrative comes to full stop to give way to a long exposition on how he got a scar on his leg. It happens often, modern readers can't take it. Another example is when they're at the thick of battle with Greek ships burning and you get a full pause to give detailed account of ancestry of several leaders, many which you only see the name once. It's like Homer is concerned with one thing and modern readers with another. But as far as the actual story, I could summarize for you in a few paragraphs, it's not a complex, subtle story. It's a story about betrayal and revenge, heroism and cowardness, loyalty, adventure, violence. It doesn't hide its meanings from you at all. Hell, those poems were suppose to be as straight foward as possible, after all, they were made to be memorized.
And Homer is the difficult one, Beowulf and Gilgamesh are even simpler "way less characters to begin with".