Guardian Types are like a template you apply on top of the default stats of a Guardian. The baseline stats are shown by a Cool Type guardian. The stats of the other Types are then adjusted up and down according to the table below.

Which Type is most desirable really comes down to what kind of Guardian you have, and what you want to do with it. A good general rule is that Types that increase natural advantages are more desirable than Types that cover natural weaknesses.

The Type for Guardians captured in the Hunting Ground and Coliseum are random. Invitation Reward Guardians are always Cool.

When you Rebirth a Guardian using the same Type for the base and sacrifice cards, the reborn Guardian will have have a new Type.  The new Type still affects the same stats as the original Type, but has higher modifiers. For example, a Chaotic Guardian has +10% HP and -10% WIS. When you Rebirth it by feeding it another Chaotic Guardian, the Type changes to Bold, and the modifiers change to +15% HP and -15% WIS.

Rebirth will not have any affect on stat modifiers for Cool and Ace Guardians.

Guardian Types
Ace +10% +10% +10% +10% +10% +10%
Chaotic +10% - - - - -10%
Bold +15% - - - - -15%
Sexy -10% +10% - - - -
Erotic -15% +15% - - - -
Powerful - - +10% - -10% -
Berserk - - +15% - -15% -
Brave - -10% - +10% - -
Stalwart - -15% - +15% - -
Fast - - - -10% +10% -
Sonic - - - -15% +15% -
Intelligent - - -10% - - +10%
Wise - - -15% - - +15%
Cool - - - - - -
Boosts all stats. The most desirable type, but also less common than the others. Often costs significantly more during trading. Ace Type does not change through Rebirth.
Chaotic and Bold
Increased HP, decreased WIS. Excellent for cards such as Titan or Gargantua with naturally high HP and physical attacks. Poor for Guardians with elemental attacks.
Sexy and Erotic
Increased MP, decreased HP. In the case of the Almighty, Mighty and Great Jolly Old Azi Dahaka, their MP is greatly reduced. Sexy ranks high for these Guardians. It can also be very desirable to allow low MP Guardians to cast +4 attacks more than once, especially good if the Guardian has Revival. Self-destruct also benefits from high MP, so Sexy and Erotic are decent types for these Guardians.
Powerful and Berserk
Increased ATK, decreased AGI. Good for any physical attack Guardian, especially wall cards, but at the increased risk of getting one shot before attacking. Due to its Quick Strike and Self-destruct abilities, this is a very good type for Maniacal Juggernaut.
Brave and Stalwart
Increased DEF, decreased MP. Good for Guardians with more than enough MP to cast their highest attack twice, increasing survivability without sacrificing damage. Can be detrimental for Guardians with naturally low MP, especially if they have Revive. Be careful when creating Heroic Types because it may prevent the Guardian from casting +4 abilities.
Fast and Sonic
Increased AGI, decreased DEF. Excellent for Guardians with naturally high AGI, and desirable for most other Guardians, as attacking first is a significant advantage in battle. On the down side, it usually doesn't make wall cards fast enough to make a difference and reduces their defense, making them less effective as a wall. This Type is highly desirable for glass cannons such as Almighty Jolly Old Azi Dahaka and Almighty Dagon.
Intelligent and Wise
Increased WIS, decreased ATK. Ideal for Guardians with naturally high WIS and elemental attacks. One thing to remember is that after Guardian with this Type run out of MP, its physical attacks will be even weaker.
All standard stats. Generally considered an OK type, but has no strengths (and no weaknesses). Cool Type does not change through Rebirth.