When you start a new game of Animal Crossing Wild World can you control what fruit you get, hair style, etc.?

Yes you can. A character called Kapp'n will ask you questions. Depending on how you answer them, your character will look different. You start with a default shirt. Your hair colour and style can be changed if you pay. You can buy new shirts. You can get fruits from other towns, and the original fruit is randomly generated as far as I know.