headphone out = use mini to mini
-you don't get the 'purest' sound from the headphone jack just because the audio signal is routed through several connections before reaching your amp
ipod line out dock
-theoretically, this gives the 'purest' signal because the line out dock bypasses the ipod's internal amp and goes straight to your amp
Many types of wire available, typically, solid siver, stranded copper, silver plated copper (SPC), etc.
Most people who go the portable route, like to go with stranded wire for durability/flexibility (usually copper or SPC wire) just because solid wire is more susceptible to being damaged if it gets bumped/banged/bent/etc. a lot.
As for which wire gives the 'best' sonics, that is hugely up for debate and depends entirely on you and your ears. The more exotic the wire, the higher the price will be (don't intepret exotic = better!). Depending on what type of line out dock you need (LOD to mini, LOD to rca, etc.) I wouldn't spend more than $100 and even that's pushing it.
Think about it, would 3" of wire really improve your set up? Spend it on headphones/ear buds instead
Hope this helps.