If you are just starting out in photography/video, I would get the 60D or T3i and invest in some lenses.
I have had a 60D for more than a year and it is a great camera. Haven't used it much for video though. I have 15-85 EF-S, 10-22 EF-S, 24-70 EF, 70-200 f/2.8 EF II, 50 f/1.4 EF, and 85 f/1.8 EF. My pre-ordered 5D III just shipped today.
The 5D III will be better in low light. Should be able to use 2-3 stop higher ISO and still get acceptable results. The 5D III also has a much better auto focus (AF) system which will track moving subjects better and work better in low light than the 60D. However, the better AF does not help with video. No DSLR has a video AF that really works while you are shooting video, ie track you subject while you pan. Some claim to have active AF while shooting video, but none that I have seen are usable. They all will hunt for focus while shooting video, which is acceptable for armature video of your kids, but looks totally unprofessional.
The sooner you get a camera + lenses, the sooner you can start shooting and learning.