Scanning negatives is often the best route, but to do this you need a scanner with a light adapter (to shine light through the negs) and a proper film mask. A variety of scanners support this. If you only want to scan negs, and are willing to make an investment, I hear that the
Plustek OpticFilm 7200 is a good choice. Otherwise, you'll have to find a flatbed scanner that supports scanning negatives.
I've also had some luck scanning prints, but with matte prints you have to watch out for little white dots that can appear on the image while scanning, and with glossy prints you have to watch out for finger prints and etc. I prefer scanning matte prints.
If you're going to scan your prints, try asking for matte next time instead of glossy, and see how those scan.