For the most part it doesn't matter.
If you want to get technical...
You choose the thickness of the copper wire by the amount of amps you need.
You choose the thickness of the insulation by the amount of volts you need.
You choose the type of insulation by the conditions the wire will be installed in (I.E. temperature, humidity, ect.)
For ampacity, see this chart --> http://wiki.xtronics.com/index.php/Wire-Gauge_Ampacity
(look under CU Max enclosed Amps)
So...to..summarize ANY wire insulation can handle 12V. ANY wire insulation can handle the temperatures and conditions inside your case. The only thing you care about is ampacity. I would go with 22AWG multistranded or bigger just to be safe. Most power supplies use 16-18 AWG.
Radioshack would be your best bet. Homedepo and Lowes also carry wire, but you might have a limited selection with the smaller AWG's.Edited by crimsontears809739 - 1/31/13 at 9:41am