I agree with dedhed, but the 16yo likely isn't growing much more, and will likely fit an adult bike. 14yo, absolutely depends on how tall she is. I second looking at your local used market (whether it's craigslist, kijiji, used(yourscityhere).com, or whatever.
Pinkbike.com buy&sell can be good for used mountain bikes as well - not a lot of dirt cheap stuff on there, but a lot of quality bikes.

I'm not really a mountain bike guy, so can't get into the merits of specific models. I will suggest, depending on what kind of trails you're planning on doing, a cyclecross, gravel, or adventure bike would be more versatile if they want to use it for road riding, commuting, or dirt trails. Just no suspension, so not really suitable for extreme terrain.