Based on your experience in analogue B/W photography, colour adds another component to your work, though the process is similar yet sophisticated in many ways:

Unfortunately, as you just observed in your family pictures, the colour of prints fades during the years. The colours change depending on the process. If you would like to know more about the details, click here for a good overview.
Scan your film in the desired resolution and you will be able to retain and adjust the colours. Though – colour film scanning is a bit tricky due to the orange mask…
With the Epson V 700 scanner (please find the manual here), you could use the Epson Software or VueScan, depending on your liking. For any of them – NEVER EVER use the full auto-mode!
With the Epson software, it is comfortable to work with the histogram and adjust your image. Vue Scan has a library of film types which might be a good
– safe your image uncompressed!
– back the originals up!
If you’re keen, try to optimise your image using luminosity masks to leave the highlights and blacks untouched. Here is a tutorial.

For developing your slide films, you might collet them and send them to http://www.analogfilmlab.com
Please see an overview of different film types, exposure and development here.