Yes, you'll need something to connect your ipod to your amp. There are a couple option: (1) a short mini-to-mini interconnect, which uses 3.5mm male plugs on either end; or (2) a line-out dock (LOD) to mini interconnect. The first choice will work with both your computer and your ipod. The second will only work with ipods with compatible dock connectors. I'd therefore suggest you go route 1, then decide if you want to try the second route for slightly better sound out of your ipod.
If you don't have a mini-to-mini connector, the easiest way to get going is your local Radio Shack. The next step up would be a Cardas mini-to-mini that a number of retailers who are Head-fi sponsors carry. It has some em & rf shielding and uses higher quality wire and connectors for very little money. Then there are a whole range of upgraded interconnects, with increasing levels of controversy as to whether or not they make a difference, and if they do whether or not they are worth it. My advice is to start basic, get to know your new equipment, then consider alternatives.
You should only need a 6" interconnect, unless you have some reason to not have your amp & source next to each other.
Someone who owns the DT880s will have to chime in on whether or not you'll need an adapter to plug into the female 3.5mm connector on your amp. I think the DT880s have a 3.5mm (1/8") plug w/ an adapter to use with larger 6.35mm (1/4") plug. If so, then you are fine on that end.
Happy listening. I haven't heard your cans, but I think you'll like the mini-3.
