I think the good thing about Harry growing up with such horrible people was that he wasn't spoiled, he didn't take much for granted, he saw how horrible it was being bullied and he never went down that road, instead he found himself helping more, and even when he found out that his dad bullied Snape, he was a bit shocked and that just shows that he had taken his living situation and grown into a great person.
I never actually thought about James influencing Harry into bullying. I imagine Harry and Snape probably would have had much more fights, and he would have had more detention, if James was around because Harry may have thought he had that extra back up. Or a bit of extra information to start taunting him

but instead, he never knew about any of that until the third/fifth year, so he never knew that James was the reason Snape treated him the way he did.
As a reader I really feel for Harry that he not only had to grow up in a house that hated him, he grew up in a house that hated his parents. I know it's hard for a child to grow up not knowing their parents, even if they were adopted and their parents knew nothing about their parents. But for Harry, he was never allowed to talk about his parents. He knew his aunt and uncle knew about Lily and James Potter, and they could have told him stories about his parents, but instead they didn't tell him anything. I just think that's emotional neglect, leaving Harry in the dark without knowing anything. I would feel so angry if that was me, that there was all this information about my parents that people refused to tell me because they didn't like them (or me).

Poor Harry
As for Sirius, I was so happy when he came onto the scene and explained everything. I think I cried! And it was such a happy moment, and for a while I was thinking about the life they would have together when Harry could leave the Dursleys to live with him. I was also really upset when he died, because when Sirius called Harry James I felt like he was just his substitute for his best friend. Although, I know that isn't true because the times they met before that he treated Harry like his Godson, or perhaps Nephew. But I think he expected him to be just like James. And then Harry had once again lost someone with such a strong connection to his dad, and to a better, happier life. I was so upset for him.
And like I said, I would LOVE to read about James after Hogwarts. What he had done on the day he graduated? How had he proposed to Lily? What had happened at the wedding? What about when they moved into their first house? Did they have Sirius, Lupin and Pettigrew over regularly? How did they react and prepare for Harry's arrival. How had they been parents for that short time? So much!!