Will an iphone 4 do the job?

I'm a 14 y/o boy and I was wondering whether to film a dance competition for my school would be a good idea. Do you recommend using my phone or do I need to bring a better camera.

If there are any cameras that are fairly cheap and work WITH macs they please let me know!

As long as it's help steady etc, I've always been happy with the camera quality on the iPhone 4 but I've never needed to use it professionally

IPhone 4 should be fine. Maybe try a practice run to see if you're happy with the quality? Or look online (eg eBay, Amazon) for alternatives. Watch out for scams though - be careful who you buy off.
Hope this helped and good luck if you decide to enter the competition!