It sounds like you have the assignment to write the personals... so, a personal ad will show strengths. We always want to put our best foot forward. It will likely show a flattering physical description which you can find a little of on page 16 of the Scribner edition.
You should also note positive character traits like loyalty, sacrifice, and a care-free spirit. Think of examples from the story when Gene has been overly loyal to Finny (not enlisting), or when Finny has been entirely creative and fun-loving (making up blitzball, the Winter Carnival, and the snowball fight). I bet your teacher would like to see examples cited because we all use these assignments to check if you've read and can think about what you read. So blitzball is chapter 3, the Carnival is in chapter 9... go get 'em.
To do this, it helps to look at evidence in the book that reveals what Gene and Finny most want in life. Personal ads are usually taken out by people who are earnestly seeking something in their lives that they are lacking, that they feel will make them very happy. So we need to look at that for Gene and Finny.
Let's start with Gene. We see in the first few chapters how insecure he is, and how desparate he is to fit in with Finny. He is jealous and envious of Finny's coolness, and wants to be like that himself, even though he really isn't. He doesn't have a lot of self-esteem, as seen through is admiration of Finny and his jealousy for him. Later on in the novel, Gene wants forgiveness for what he did and thought about Finny at the beginning. He wants to take time back and undo the tree, and all of the awful feelings that he had for Finny.
Finny wants friendship and admiration from everyone. He also wants to be involved and in all of the action. Later on, this manifests itself as he reveals that he wants to be in the war, and has been trying to enlist. He wants everyone to be happy, and enjoys having a lot of friends around to have a good time with. Later, he of course would hope to have his healthy leg back again. He also wants to challenge himself in all things.
So, their personal ads need to reflect those desires and intentions. Parts of Gene's could read "Young male seeks confidence and self-esteem. Desires coolness and popularity, along with perfect grades. Somehow, a perfect balance must be achieved." Or later on, for him, "Young male seeks forgiveness for past mistakes. Please respond if willing to offer friendship and forgiveness." Finny's could read, "Young, athletic male seeking challenges in the sports world, as long as they remain anonymous. Also seeks team of players to enhance his own abilities. Admiration is a plus."
I hope that those thoughts help to get you started and on the right track--good luck!