iPod Classic 7th Generation
Beyerdynamic DT-770 250 OHM
Now the issue I'm having is which portable amplifier is better and more powerful to drive the cans while pairing and sounding well with the iPod Classic.
Any help would be appreciated.
Both would do just fine. IMO the C5 is a little more analytical in its sound while the E12 is a touch more fun. Neither would have a problem driving your Beyers and both offer adjustable gain and nice smooth volume pot.
If I had to pick, I'd go with the C5 as it's a little closer to the iPod in size, so making a stack would be a little easier.