I've shot both high school and college gymnastics for well over 20 years now. The most important thing is to get in as much light as you can, ie, fast lenses. I started off back then with a very slow 75-300 f/5.6 lens, then upgraded to a constant 70-200 f/4 lens. This was in the late 80s. (Non Canon make). Then went for a 80-200 2.8L lens in the early 90s, 70-200 2.8L lens a year later.
Then threw in the towel on all 2.8 lenses. Just way too slow for the images that I had in mind - mid air leap shots that were ultra tack sharp. But back then I was shooting with Fuji 400 and Fuji 800 press film.
My main lenses now are the 200 1.8L EF and the 85 1.2L EF II with a future upgrade to the 200 2.0L EF IS on the way. The 85 1.2L EF II is a great lens when coupled with a faster focusing Mark 3.
The f/stops make a HUGE difference.
They don't allow a flash for any high school or college gymnastics event. It's against their rules and grounds for you to get kicked out of the event.
At the very least, the 135 f/2.0 will get you some very decent shots. I've seen many 40d rigs coupled with this lens. The 85 1.8 is also good.
Funny story - my buddy and I (I'm shooting a mark 3, he's with a Nikon D3) were both at a college gymnastics event. There's a person in the crowd that fires off a flash and the officials come to us and say "no flash use". I looked at her and pointed to the cameras - "Does it even LOOK like we need a flash?!?!" I'm using the 200 1.8L EF and he's with the Nikon 200 f/2 AFS. Then I pointed to the crowd behind us and said to her "I'd suggest looking there first...we're not equipped with flashes." The official walked away highly embarrassed.
She was one of those ladies that always seems to have a chip on her shoulder. If she was one of the students (and was cute) then I would have educated her, gotten her phone number, set up a date and then send her on her way to find "the flasher". 