Draco Malfoy:

Malfoy made Dudley Dursley look like a kind, thoughtful, and sensitive boy.

Every child hero needs a competitor, someone who makes his life a living hell but isn't necessarily the person who's planning to send the hero to hell. In Harry Potter's life, Draco is the person who's more than happy to fill this position.

From trying to get Harry and Ron expelled during their first term to trying to knock Harry off his broom during Quiddicth matches, Draco despises Harry Potter and his friends, Hermione Granger (Muggle-born and therefore is unworthy to live.) and Ron Weasley (Pure-blooded but poor and a muggle-lover and therefore doesn't deserve to live either.)

When it comes to Ginny, Draco probably doesn't even know what her name is, that's how inconsequential he perceives her. She's a Weasley first and a stupid girl in love with Harry Potter the second, and to him that's all she is... for now.

Ginny Weasley:

Ginny who had always been very taken with Harry, seemed even more heartily embarrassed than usual when she saw him...

The seventh child and only girl of the Weasley family, Ginny has a lot to live up to. Three of her brothers were some of the most popular students at school, two were head boy and Ron is the famous Harry Potter's best friend. So far all Ginny has done is wreak havoc on the unsuspecting residents of Hogwarts during her first year when she was possessed/manipulated by Tom Riddle.

Ginny is probably on of the most underdeveloped semi-major character in the books. Few of her characteristics are presented and aside from the incident with the Chamber, the only thing readers know about Ginny is that she has an on going crush on Harry Potter. Because of her feelings for said hero, Draco Malfoy, Harry's adversary, becomes her enemy as well.

As far as personal fights go, the only time Draco and Ginny has come face to face was when Ginny stood up for Harry in the book shop before her first year, so far no other fights has taken place... So far.