I have a 14yo daughter. I think body weight exercises are plenty for a beginner. Is she interested? Maybe start really small, like minuscule. Just one plank off every day. Once she can hold it for a minute, maybe move to a push up challenge. My DD was very interested in heavy lifting, but she hated the gym. All those half dressed grown men were so distressing, that she only lasted about 2 months. Make sure you know what you're doing before you spend the money.
Is there any way you could take some kind of self-defense training with her? That would be very useful excercise for a teenage girl. Tell her you want her to get to the point she could kick your ass, lol.
CW-125, part calorie counting, part transition to primal
GW- Goals are no longer weight-related