It depends on the pet actually. For example, if you are going to use it as a tank (like a cu sidhe) you should go for hp first. But if you are going to use it to deal high damage as much as possible, you should raise strength and stamina first.
About the relation between str/dex/int and hp/stam/mana; I have experienced that increasing strength does not increase hp as well. But increasing dexterity and intelligence will increase stamina and mana automatically (as long as stam ≤ dex and mana ≤ int).
I have to mention something buggy though, having traits like stam and mana bonus ruins that relation unfortunately. Kane has updated the stam and mana bonus traits lately, I am not sure if they are still ruining it. You can send me a PM from here or ingame about pets and such, anytime. I will do my best