I think you've all nailed it. Hagrid definitely was the right choice to be Harry first "wizard" friend. He's extremely kind and helpful. He helped out Harry gi-normously from telling him where the best place is to get a wand to telling him what the first task was in the Triwizard Tournament. Without Hagrid, there were times that Harry could've died without his help, although there were also times Harry could've died with his help (*cough* the spiders *cough*). Also, Hagrid gave Harry HEDWIG for his birthday and Hedwig became the loveable bird that helped Harry through the summers at the Dursley's.

Hagrid was family for Harry and it helped that he knew right from wrong. He helped out Harry so much and I would definitely say that they were more like brothers, not father and son. They confided secrets in each other and Hagrid was one of the big factors in Harry loving to come to Hogwarts. He was also a relief in the school day, I bet. Having tough, hard classes where the teachers are often strict or don't have much of a funny bone probably wouldn't be fun for anyone. So, having a fun, extremely friendly teacher like Hagrid probably always made Harry happy.

Basically, the equation is: Harry + Hagrid = a great life for Harry and Hagrid alike. They both had huge impacts on each others lives. Harry was just the student Hagrid needed to cheer him up when he was down, and vice versa. YAY HAGRID!