Scanner

The maximum optical resolution of a scanner is very important. Be careful of claims of 'interpolated' resolution--this is a software trick to try to generate a larger image from less data, but cannot really generate a clear image. Also, the real limit is the lower of the vertical or horizontal maximum resolution, anything past the lower of those two numbers is using interpolation.
The amount of resolution actually needed depends on the intended job. Scanning something purely for use on a computer screen at about the same size needs a mere 75 dpi, but this about the least demanding job possible. If you intend to print your scanned image, a minimum of about 300 dpi is needed for color (and 600 dpi for black-and-white).
The above assumes that the final image should be about the same size as the original. For enlargements, better resolution is needed so that the final image maintains the required dpi after the image is enlarged. For instance, to print a 4"x5" photo at the size of a full sheet (8"x10"), the 8"x10" image will need (300 x 10) 3000 pixels down the long side. That turns into (3000 / 5) 600 dpi for the original scan.