We bought a Sony HDR-CX-430 last Spring. It has optical image stabilization which means that even if it is windy or you aren't holding it perfectly still, the video won't be shaky when you play it back.
My DD has been a performer since she was little and we have taken a lot of videos of her performing as well as taking video at WDW/DL and other places. I am so bummed that we did not have this camera when she was younger. There is an incredible difference between our old Sony and this Sony. The videos are far superior on the new one both indoors and out and in bright or low light. It also has an incredible zoom and does not lose quality with the zoomed footage. It does an amazing job. DH, who is not remotely a professional, took an archive video of a show with it for DD's theatre group and it looks professional. Of course, it was on a tripod and not hand held for that, but he had done that once with our old camera for them and this video is far far superior.
If you look around the internet, I think you will find it gets very good reviews. I think the camera itself holds about 2 hours of video, but it takes memory cards which is what we always use so that we can easily transfer and also keep the memory card with the video on it if it is something special. I know this summer had had about 4 hours of video on one memory card- so you can get whatever size memory card works for you. I can't say enough good things about this camera!