If my wand could change one thing about my family I would change the past so that Voldemort would never have killed my parents. They would still be alive, and I could live a normal life. Well, normal for a wizard.
We would continue to live in Godrics Hollow, my parents and I. I would never have to live with my aunt and uncle, which would suit us all just fine. I would not be 'The Boy Who Lived' or 'The Chosen One'
If this was reality, I would still want to be friends with Ron and Hermione. I would invite them to my house, and hang out there instead of only being able to hang out at the Burrow. I could be happy, never having to deal with Dudley, or being hated by those who I live with.
Never having to be seen as a mistake to those around me. I could get to know my parents and know what they think about the things I do at Hogwarts, or the friends I have.
I would also get to spend more time with my godfather as well. We could do a lot of things together, my father and Sirius could tell me about their time at Hogwarts. The things they did, other people they knew.
They could teach me useful spells they know, while I spend the holidays at home with my mother, father, and godfather. We could spend time at Grimmauld Place.
My life would be a lot better if my parents had not died that fateful night.