Hello bobrobinson,
Welcome to the Q&A Board!
The quality, not the physical size of a lens, is a very important factor in the quality of images a camera takes. To be honest, unless you buy a real cheapo camera, most digital cameras have a very good lens that should take fine photos. Obviously, a $250 camera may not have the lens quality of a $1000 advanced digital camera, but it will produce fine images for most of us.
What
will take better photos as far as the lens is concerned, is if you use the optical rather than the digital zoom. Most cameras have both optical and digital zooms (only the least expensive have only digital zooms). Digital zooms are not true zooms, so the optical zoom is the zoom of choice. I avoid using the digital zoom on my camera.
You can learn about the important differences between digital and optical zooms here:
http://www.digicamhelp.com/digital-camera-features/digital-camera-lenses.htmPlease let us know if you have additional questions.