Griffy and Dinoceros are both super OP and trivialize most of the game so if you want a challenge I'd skip them.
Really anything in their 3 compatible genus are good enough to beat the game, i.e. Milites/Dracones for Oliver, Aves/Aqua/Flora for Esther, and Beasts/Mortui for Swaine.
For Oliver I use Mermite (one of Mitey's final forms), Splatterhorn (Bighorn final form) and Puss-in-Boats.
For Esther I use Electrongo (Drongo final form), Grimray, and last spot is usually filler - Esther is pretty poor AI with anything but her Drongo - so just boost the crap out of it's Magic Attack and fill it up with Storm spells.
For Swaine I use Bone Brigadier (Bonehead final form), the Monkey thing you get before the first dungeon (one of his final forms - Aye Aye Catcher, gets Raise, and it's in the Beast family), and Grimpaler. Swaine's starting familar is really bad and isn't even in one of his 3 genus.
Grimpaler (Shrimpaler final form) is super sick - has 5 star attack speed.
Also, what does it mean when a pet has a double sign? Like Double Water instead of Water? Does it mean they have a higher cap, or easier to level, or more powerful? Or does it not have a significant effect?
Sun: +5% Resistance to fire and sleep, +20% damage to moon/double moon, -20% damage to star/double star
Double Sun: +10% Resistance to fire and sleep, +30% damage to moon/double moon, -30% damage to star/double star
Moon: +5% Resistance to water and confusion, +20% damage to star/double star, -20% damage to sun/double sun
Double Moon: +10% Resistance to water and confusion, +30% damage to star/double star, -30% damage to sun/double sun
Star: +5% Resistance to storm and poison, +20% damage to sun/double ssun, -20% damage to moon/double moon
Double Star: +10% Resistance to storm and poison, +30% damage to sun/double ssun, -30% damage to moon/double moon
Planet: +5% exp bonus, +50% damage to double Planet
Double Planet: +10% exp bonus, +10% damage to sun/double sun/moon/double moon/star/double star