How high a resolution you use will really depend on what you want your family to do with the pictures.
If you're just sending them the pictures and they don't plan on having them printed, you can go pretty low (and a small file). Stick with either .jpg or .gif files. (these can be opened in a person's web browser if they don't have special software. You can also choose the resolution when you go to save these files and how much you want them compressed (made smaller, which means quality will go down slightly.) Try playing with the files and save several versions until you've found a happy medium between quality and size.
If you want to send a really high-quality photo so they can get it printed, you will need to make sure the resolution is higher. Remember though that some internet service providers will not allow their clients to recieve a very large file through email.
One option is to look at some of the photo places on the web. You can upload photos to these places at fairly high resolution for free, people can view the photos for free and if they want pictures, they can order them from the online place for a pretty good price. Some good places I've used are Ophoto and Imagestation.
You might want to check out Sony's ImageStation:
http://www.imagestation.com/
I've ordered from them before and been happy. You can also include a password on your album on these sites so you don't have to worry about strangers being able to see your pictures.
As a general rule though, most scanners will scan at a higher resolution than you really need for an acceptable quality photo, especially if it's just being viewed on a monitor. If you're going to just view on monitor, try scanning at about 300 dpi. If it's going to be professionally printed, you could go about 600 dpi and probably be more than happy. But again, scan these at different dpi-s and find what you're happy with.
And finally, (sorry, didn't realize it would be this long) you may be able to take your film to
Walmart or Sams and get them to create a CD for you with all your pictures on the CD for a pretty cheap price and save yourself the trouble of scanning all the photos.
rachael