Yup, green stats are good. You get them either from genetic power or from genetics.
Genetic power or descendant of heroes is when you breed pets that are level 50 with each other. Their offspring are 1st generation or 1 star pets.
Then you level that pet up to level 50 and breed it with another level 50 GP1 pet. This gives you GP 2 offfspring. And so on up to GP three.
Each GP or "Descent from Heroes" adds ten points to all your pet's stats, which gives it much better chance in battle.
Some genes increase one or two stats, or increase one stat at the expense of another. Light bones lowers Constitution and increases Agility.
Some genes only lower stats, like Dystrophy, Weak Jaws, Fragile bones, or Thin skin.
Good genes that improve stats are Diamond horn, Sharp Teeth, Steel muscles, Steel Bones, Hound, Thick skin.
Acute eyesight gives you further sight on explore. Animal instinct increases critical strike chance.
Magic horn, fearsome look, ice aura, blizzard an massive wings make your opponent in a fight miss their turn.
Poisonous teeth, poisonous claws, venomous skin, napalm gland (if your dragon also has fire breath) all lessen your opponent's hit points by half each turn when they activate.
Magic mirror reflects your attack back at you.
Song of peace prevents your opponent from going beserk and also you can win one battle in explore without fighting per map, although you get no XP from it.
That's all I can think of.
Whoever calls on the name of the Lord shall be saved.
Random acts of senseless kindness.