I would say Legend for dystopian, Eragon for fantasy, or Enders game for sci fi. When I was younger I really enjoyed Percy Jackson as well. I don’t know if it holds up for 13 year olds though, it’s a little juvenile and you kinda have to grow up with it to like it, but it might be worth a shot. It got me into reading when I was 9-10
Here’s some I really loved at that age, with my Fantasy/Sci-Fi bias: Warriors (Erin Hunter), Graceling (Kristin Cashore), Airborne (Kenneth Oppal), Ranger’s Apprentice (John Flanagan), The Two Princesses of Bamarre (Gail Carson Levine), Howl’s Moving Castle (Diana Wynn Jones), Animorphs (K.A. Applegate), The Tombs of Atuan (Ursula K. Le Guin), AND OBVIOUSLY The Hobbit x1000000
If she likes romance, Sarah Adams is closed door but idk about other adult themes. The Firekeeper’s Daughter is like a YA thriller with indigenous rep. Truly Devious and A Good Girl’s Guide to Murder are YA true crime (third Good Girl’s Guide is pretty dark tho so her mom should check content warnings before she buys her the series)