This is quite an old thread but hey ho..
Shoot in P mode (programmed auto), leave it alone with the flash off and shoot away, thats perfect for snapshots. You can adjust the shutter speed and aperture in this mode also, its kind of like having aperture priority and shutter priority all rolled into one.
Having a faster lens is also a good way to improve your pictures and how they look. A fast lens, low f number, will give you better performance in low light situations, but also create nice shallow depth of field (blurred background with your subject in focus). The lower the f number, the blurrier the background will become.
The kit lens you have will be f/3.5-5.6. A good prime lens (no zoom) which is a 50mm equivalent, would be excellent. Everyone should have a 50mm equivalent lens. These lenses are quite cheap but are fast, go down to f/1.8. You can create some great shots with them. Also the pictures will be alot sharper and have better colours. I believe for your sensor size a 35mm prime lens is what you would require.
The following picture was shot at f/1.8, nothing special just a test shot. See how the background is slightly out of focus making the subject "pop" out of the picture, gives a great 3D effect. While this can be achieved to some extent with a slow lens, its much easier and looks alot better with a fast lens. Can really play with the depth of field.
So basically i would recommend getting a 50mm equivalent prime lens. Will make you a better photographer, its the classic focal length and they produce great, sharp images with great depth of field control.