Both approaches have their advantages. Reading allows more opportunity for pausing and reflecting, but listening to an audio version with a skilled narrator is very valuable.
I have listened to several ancient Greek works narrated by Charlton Griffin; I think his voice is fantastic. Here’s his unabridged reading of the Iliad: http://www.amazon.com/gp/product/B001PU0UOA/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B001PU0UOA&linkCode=as2&tag=thewesttrad-20
If you’d prefer an abridged Iliad read by Shakespearean actor Derek Jacobi, try this performance of the Fagles translation, which is quite good: http://www.amazon.com/gp/product/B004H1Y0RW/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B004H1Y0RW&linkCode=as2&tag=thewesttrad-20
You can find comparable renderings of the Odyssey as well. These links have samples so you can hear a few minutes of the narration.
I hope this helps!