I take it that the autofocus mode can be turned off?
You'll have as much control you want. Autofocus can typically be switched of at the body, at the lens, or simply overridden by grabbing the focus ring even when in autofocus mode. You can do full auto, aperture priority, shutter priority, fully manual or whatever.
The camera shoots two formats: jpegs and RAW The camera can shoot both at the same time. RAW gives you much more control over the final image. I believe you get basic RAW conversion software in the D60. You can also do substantial post-processing in the camera, if you wish. People tend to use their favorite software for manipulating images, ranging from free to very expensive.
The D60 kit lens supercedes the one with the D40x and is reportedly much better, though I haven't used it.