If you were to print the image at three times the size of the original photograph, this suggests an absolute maximum scanning resolution of 800 spi. If enlarging small images is going to be a frequent occurrence, a higher resolution scanner will be needed to compensate for it. If this is only an occasional need, getting a larger photographic print or sending the occasional exceptions to a service bureau might be more economical approaches. In any of these calculations, only the true hardware resolution is significant. No more information can be created by interpolation, so scanning at the higher values is mostly a delusion.
Dynamic range is the biggest single element.
This means the range of original colors, from stark white to dead black, that the scanner can identify and properly write to disk. The greater the dynamic range, the more likely you will be able to maintain shadow and highlight detail. The greater the dynamic range, the more different colors or grey values in the file, and the more enhancement is possible without posterizing other elements of the file. The CCD arrays that are used in flatbed scanners have much more trouble recording detail in deep shadow than in the midrange or highlight areas. Originals with significant detail in deep shadow are candidates for the service bureau, where the photomultiplier tube in a drum scanner can dig out more information than any but the best flatbed.