Actually, there are two different ways to get Poseidon as the Bearer’s father.
If the Bearer did kill Saxon, then they do need to have Strength as their highest stat by a certain point.
if the Bearer DIDN’T kill Saxon, then they will always get Poseidon as their father, no matter what their highest stat is.
As for who my favorite father is, it’s also Poseidon. From a gameplay view, Poseidon Bearers can be somewhat more diverse in terms of stats due the way Poseidon is obtained, which gives me more room to develop the Poseidon Bearers with different types of strengths.
From a story view, Poseidon feels like the most neutral of the possible fathers. Yes, the fact that he seems to not automatically take a side does make it come off that one of his likely flaws is indecision, but it also come off as the fact he can see things with a somewhat more clearer picture out of all the possible fathers. He also seems like he has the least selfish reasons for wanting to bond with the Bearer, so the family situation also feels the most stable with the God of the Sea.
But, story-wise, Hades and Zeus also are interesting in their own way.
From a drama perspective, it is definitely Hades that seems the most interesting. He’s already got something complicated going on with Persephone and Athena, but if he ends up being the Bearer’s father , Priscilla also gets added to the mix in some way. There’s also the fact that he had been part of the Bearer’s life for most of their childhood, only to disappear for a good number of years and just suddenly come back as Hades. Adding the fact that he’s their father in this case, and the Hades Bearer certainly has the most reasons out of all the Bearers to possibly have a rather rough relationship in the beginning with the God of the Underworld.
From a family development view, I find myself the most curious about Zeus and how being his child will effect some things. Like, I wonder if it is even possible for the Bearer to develop a strong familial bond with the King of the Gods or create a sense of kinship with Zeus demigods (who are extremely competitive with each other for their father’s attention). And it’s possible to get a even more in-depth look into Hera and how she reacts (and, very likely, tries to hinder) the Bearer while they are on their journey.