You're going to find this a pretty expensive hobby. I won't go into longer telephoto lens since you just talked about indoors. Yes, the kit lens is good, but it's not a good low light/indoors lens. You have two options, you can buy another lens in that same focal length, that also has image stabilization, and a large aperture(F2.8) but that will cost you as much as the T2i alone. The other option is buying an external flash, which will still run you $220 or more, depending on how much power you want.
The video part, I'd say to get a tripod, especially with the low light areas. If you don't plan on needing a lighter tripod then you could probably get a decent one for under $100.
I'm looking to buy the Canon t2i. I am a newbie and have some novice questions I'd love your feedback on!
I am most interested in taking indoor portraits with the t2i. I know the kit lens is a good place to start, but is there a second lens that I should consider getting?
Second, I'm a musician and would like to make short good looking live videos with the t2i. I've read that I would need an additional lens for this. What do you think? Again, my shooting conditions would be mainly indoors.
Are there any other add ons you would consider essential to maintaining the t2i properly?
Lastly, do you recommend buying a three year protection plan additional to the camera warranty?
This is all new territory for me so thank you very much!