The Sony E 18-55mm OSS kit lens works very well for video, and everything will work automatically with that lens if you want the camera to do everything automatically (which makes a lot of sense for video if you're just starting out). It does image stabilization in the lens.
Any manual lenses you buy for use on the NEX with an adapter will not have image stabilization. The NEX cameras don't have image stabilization in the camera, so you have to find lenses that have it built in. Image stabilization will only work on lenses that the camera can use in automatic mode, such as the Sony E lenses, the Sony A lenses (this requires a special Sony adapter, the LA-EA1 or LA-EA2... the only company that makes Sony A lenses with image stabilization is Sigma, and they have already stopped including image stabilization in their newest lenses), and Canon EF lenses (there is a company called Conurus that makes an adapter that makes image stabilization and automatic exposure possible, though autofocus doesn't work).
When you are using a manual focus lens to take still images, you can use aperture priority mode and the camera will automatically adjust the shutter speed to make sure that the camera takes a perfectly-exposed image. That means you don't have to worry too much about the "f-stop" setting the lens is on when you take pictures. With video you don't have this option, because the camera absolutely has to get enough light every 1/60th (1080p60) to 1/24th (1080p30 or 720p30) of a second to record a frame, otherwise the video will be too dark. The only way to make the video brighter is to either turn the lights in the room up, or open the aperture up. You should adjust the f-stop on the lens until the video's brightness is at a comfortable level. Again, using a lens that supports automatic controls makes this much easier, because it can adjust the brightness of the video on the fly using the aperture. I use the Sony E 18-55mm OSS kit lens with my NEX-5N when I'm shooting video, because the camera does a great job of handling autofocus and exposure control, which is way more than I can say for myself!