What's your budget? If you can afford it, I'd probably recommend a Canon 17-55mm f2.8 (EF-S) -- Full disclosure: I own one myself -- because it's reasonably wide (so you can shoot with the camera relatively close to you/your subject), but still has a decent amount of zoom/reach if you need it, reasonably fast/bright (so you can shoot indoors), and reasonably priced (considering both of the aforementioned capabilities).
But if that's out of your budget, there's Canon's 18-55mm f3.5-5.6 (EF-S) (STM) which is much cheaper because it's much slower/darker (so you may have problems shooting indoors without additional lights). However, the STM version of this lens does have an advantage in auto-focusing when shooting video on a 650D, not a 600D. So, if you upgrade to a 650D (which I would recommend you do, if you can afford to -- full disclosure again: I own and shoot video on a 650D), an 18-55mm STM lens would be worth considering.
Having said all of that, I would strongly recommend against shooting video on a DSLR in your case. Instead, I think you'd be much better off with a ("pro-sumer" level) camcorder.As I've said before
, most people would be - Mark