How does her early encounter with Peeta affect their relationship after they are chosen as tributes?

That depends. What do you mean by first event? If you mean the cornucopia, then it makes Katniss become angry/annoyed at Peeta. If you mean when he joins the Careers, then it makes Katniss hate Peeta and wish for his death. If you have a different event in mind, you need to be more specific.