wiring a arduino led project
When choosing wire for your project the main consideration is the amount of current. Second would be the distance. 

For LEDs the current is generally low (milliamps) so something like a 20 or 22 gauge wire would be fine. You should be able to get it at a local hobby electronics shop or Amazon of course.

FYI, Wire gauge numbering is such that the lower the number the thicker wire. Thus 20 is thicker than 22. 

You may find this AWG (American Wire Gauge) table helpful: http://www.powerstream.com/Wire_Size.htm