Quezacotl
Elemental: Thunder
Starting Level: 1
Starting HP: 300
Where do I get it? Go to the classroom on the second floor of Balamb Garden and access Squall's study panel from his desk. Select the 'Tutorial' option and Quezacotl and Shiva will be added to your GF list.

GF Attack: Thunderstorm
-
Best if used against machines or robotic enemies.

Most Useful Ability: Probably Card Mod. This lets you refine cards into things that'll help you refine your weapons into the good weapons and into things that'll teach Quistis new types of Blue Magic.

There's also the Card ability which lets you change enemies that you find into cards that you can use in your deck. This is more useful at the beginning of the game when you have a wussy deck.
Ability List
Ability

HP-J
Vit-J
Mag-J
Elem-Atk-J
Elem-Def-J
Elem-Defx2
Magic
Draw
GF
Item
Card
Mag+20%
Mag+40%
SumMag+10%
SumMag+20%
SumMag+30%
GFHP+10%
GFHP+20%
Boost
T Mag-RF
Mid Mag-RF
Card Mod
AP Needed

50
59
Learned
160
100
130
Learned
Learned
Learned
Learned
40
60
120
40
70
140
40
70
10
30
60
80
Leads To...

Nothing
Elem-Def-J
Nothing
Nothing
Elem-Defx2
Nothing
Nothing
Nothing
Nothing
Nothing
Card Mod
Mag+40% and Elem-Atk-J
Nothing
SumMag+20%
SumMag+30%
nothing
GFHP+20%
Nothing
Nothing
Mid Mag-RF
Nothing
Nothing