well, if you have any midle class flatbed scanner you can probably scan your images pretty well but only in case your positives aren't too dark (I mean - the blacks on your prints don't have big Dmax). almost every flatbed (except those nasty big and damn expensive ones in professional studios) have hard times scanning the black tones without having loaded them with noise.
but there is a simple solution - make another print - soft (one step lower grade filter will be OK), scan it and adjust the overall contast in PC to match the print. in any other way you can be sure that your scans will loose shadow details significantly.
also - always scan in 16 bit/channel mode. and be sure to have good PC screen (Eizo's L's or more expensive Samsung's LCD's are good choice - and bigger doesn't always mean better).

second option is studio re-shooting the prints with digital camera. but surely the nowdays super-mega-pixel_ultra-zoom aren't so good choice. low-end DSLR (nikon D60, canon 1000D, pentax Km) will be better (sharper lens and lower noise, better details). but it is important to equally light your prints and have them parallel to your camera.

it is important to do this kind of nasty job done well because it will be the digital files that people can see all-over-the-world, not the paper prints you can show you neighbour....