I'll second Joe's recommendation - Representations are probably the way to go. Network Analyst won't help you here - this does not appear to be a Network Analyst solution and Network Analyst does not have much in the way of display capabilities.
Representations
ArcGIS Help (10.2, 10.2.1, and 10.2.2)
There are some caveats on Representations, though. Representations take a while to figure out, so plan to spend some time learning about them. They are not something learned in a few minutes. Some of their setup is non-intuitive, and they don't always behave as expected when creating and editing. They can be very useful, but you will need to dig into them a bit before you can get rolling.
As a result, Representations are great if you plan on re-using them over and over for several maps, but usually not worth it for one-time maps that need to be done quickly.
Chris Donohue, GISP