Yes, it is very important to take advantage of your familiars metamorphoses by taming the first stage, leveling it up up all the way before each new stage and get those familiar hearts maxed. Without doing these things, your familiar will finish far weaker than if you had done these things.
I would also stay away from taming 2nd or final stage familiars unless it is for a side quest or trophy. If you are going to spend time taming a familiar then wouldn't you want to get the most out of the creature and your time?
Good luck! Feel free to message me any questions. I have pretty much conquered the games finer points.