Are you shooting all the kids, a couple kids, or just one kid or one team. That will determine how flexible you need to be - how often you can plan to change lenses.
Use zooms for floor and possibly vault. Use primes for everything else. You reeeealllllyyyy need the speed of the primes to stop the motion. Being on the floors allows you to use the foot zoom.
If you are shooting from the floor start with the 85 1.8. Remember to get shots with the kids sitting together, chalking up, stretching - close ups of just the hands, etc. Get shots with the coaches in the view - coaches instructing the kids. Get unique perspectives - camera at floor level for example.
Knowing gymnastics and the routines helps as you can time the shots. Set your ISO and shoot AV.
If you have the room (back) - considering setting one camera up with the zooms (24-70, 70-200) and the other with the primes (50 and 85). Or if you are just shooting a team - set one up for video and the other for stills. Set the video up on a tripod and use the other hand held. Need to scout locations.
A few more things - with contrasty backgrounds (think gyms with striped walls and lots of equipment everywhere) it is often hard to get a proper focus with the narrow depth of field. As I am just shooting my kid and his team - i pre-focus using the viewing screen for rings, p-bars, pommel, high bar. It my not be as hard to focus if you are on the floor.
7D | Canon EF-S 17-55 2.8 | Sigma EF-S 30 1.4 | Canon 85 1.8 | Canon 135 2.0 L | 430EX | TT Speed Demon | Sony RX100