Optical zoom is true zoom so the camera's lens actually moves forwards and back, changing the magnification of the shot while the resolution remains the same. Digital zoom, like interpolated resolution, is a product of the camera's software. When you use digital zoom the camera takes a picture then digitally crops it, isolating the part you zoomed in on. This part is either saved as is or interpolated to blow it up to regular size. Digital zoom results in lower image quality because digital cropping reduces the resolution.
Optical zoom is better than digital zoom and some cameras offer both.
If you do go for an optical zoom, the viewfinder should be coupled to the zoom so you can see exactly what you're shooting. To take extreme close-ups like photographing a stamp or coin collection, you'll want a camera with a macro mode. A macro lens can act as a normal lens but also lets you focus on an object as close as 3 cm. Macro mode works best from 10-50 cm. For the average user, autoflash is just fine.