Unless you will be shooting professional video, the kit lens will be fine. And FWIU, rots5 is talking about focus, not stabilization.
If you are shooting any kind of video with the exception of the T4i and a Canon STM lens, you will need to manually focus anytime the subject moves planes. Manual focus is a real tricky thing to learn, especially when using the kit lens and the screen in back of the camera. The kit lens has a very sensitive focus ring and goes OOF with the slightest twist on the focus ring. Also, the kit lens does not have Ultrasonic focus, which allows you to adjust the focus manually when the focus selector switch is set on Auto.
If you are planning on shooting anything but closeups in a small indoor space, or a wide angle view, the Canon 50mm lenses are a great choice.
The Canon 50mm 1.8 costs around $100, and has a aperture of 1.8 which will give you incredible low-light abilities as well a razor-thin depth of field which gives you that professional look/Bokeh.
http://www.amazon.com/Canon-50mm-1-8-Camera-Lens/dp/B00007E7JU/ref=sr_1_1?s=electronics&ie=UTF8&qid=1363099824&sr=1-1&keywords=canon+50mmStep up to the 50mm 1.4 for Ultrasonic focus and a 1/3rd of a stop larger aperture.
IMO, get the 1.8. The quality will beat any zoom lens under $1000.