What wire do I need to carry 30 A for 18"?
Over 18 inches you would drop about 0.675 volts with 18 gauge wire. 12 gauge would drop about 0.1 volts. You would need to use 6 or 7 gauge to handle 30 A over an extended period. 

If you are not using continuous current, but pulses, you could get away with using a smaller gauge wire. However an undersized wire would heat up significantly in just a few seconds. Unless you are sending pulses of less then 1 sec, you will need a large diameter wire. 

AS for the insulation, it depends on how the wire is being used and how it is routed. 30 A is a lot of current. If some one can come in contact with it, you need heavy insulation for safety. Especially if it flexes. If it is total enclosed in a non conductive housing, you could use thinner insulation.