Types of electrical wire usually separated in 3 category:

Power cable

control cable

Instrument cable.

You may familiar with some Insulation and Jacket type such as
THHN/THWN
PVC/NYLON
FR-XLP
RHW-2 OR RHH OR USE-2
FR-XLP
HMWPE, LSZH.

Here are only few cable types and their applications example:

600 V THHN Copper conductor: For use in general wiring application and power in conduit.
600 V RHW-2 Copper Conductor: For use in harsh environments for general wiring direct burial.
300 V UL type PLTC: This is a multi-pair instrumentation cable: For use in instrumentation and process control applications

Copper Electrical Wire
Copper is the common used because copper is a very good conductor, and is easy to mold and bend.

Aluminum Electrical Wire
Aluminum is cheaper and more abundant than copper. It is also easy to shape and bend.
More important for electrical designer is to select the right size of electrical wire . The following link is the method of how to determine cable size.

Electrical Wire Size

Before selecting electrical cable, There are much more but here are just some criteria s to keep in mind :

Cable conductors

Cable AWG

Temperature

Shield type

Material type

No of pairs

Electrical wire size using table 310.16 NEC2008 on page 70-148. Simply calculate amperage (current) flow through the circuit and then apply the table.

SIZE AWG OR KCMIL	COPPER	COPPER	COPPER	ALUMINUM	ALUMINUM	ALUMINUM	SIZE AWG OR KCMIL
_	TYPE TW,UF	TYPES RHW ,THHW,THW, THWN,XHHW USE,ZW	RHW-2,THHN THHW,THW-2 (90°C)	TYPES TW,UF (60°C)	TYPES RHW THHW,THW THWN,XHHW USE	TYPES TBS,SA SIS,THHW<>	SIZE AWG OR KCMIL
18 16 14 12 10 8	_ _ 20 25 30 40	_ _ 20 25 35 50	14 18 25 30 40 55	_ _ _ 20 25 30	_ _ _ 20 30 40	_ _ _ 25 35 45	_ _ _ 12 10 8
6 4 3 2 1	55 70 85 95 110	65 85 100 115 130	75 95 110 130 150	40 55 65 75 85	50 65 75 90 100	60 75 85 100 115	6 4 3 2 1
1/0 2/0 3/0 4/0	125 145 165 195	150 175 200 230	170 195 225 260	100 115 130 150	120 135 155 180	135 150 175 205	1/0 2/0 3/0 4/0
250 300 350 400 500	215 240 260 280 320	255 285 310 335 380	290 320 350 380 430	170 190 210 225 260	205 230 250 270 310	230 225 280 305 350	250 300 350 400 500
600 700 750 800 900	335 385 400 410 435	420 460 475 490 520	475 520 535 555 585	285 310 320 330 335	340 375 385 395 425	385 420 435 450 480	600 700 750 800 900
1000 1250 1500 1750 2000	435 495 520 545 560	545 590 625 650 665	615 665 705 735 750	375 405 435 455 470	445 485 520 545 560	500 545 585 615 630	1000 1250 1500 1750 2000

Apply table to calculate electrical wire size
Assume the current calculated result is 14A, cable type is copper THHN, insulated conductors rated at 90° C, and so based on the table, cable size is 18 AWG. For practical safety application, recommended power cable should be bigger than 12 AWG.