Two things: first, I agree with blue sky dreamer that scanning, editing, and cleaning up a lot of slides (or negs) yourself is a very time consuming and tedious process, especially with a flatbed-style scanner. If you want to do it yourself, I strongly recommend buying a special-purpose slide scanner, like these, ranging in price between about $200 and $2,000. Yes, they’re pricey, but sending them to a pro will be costly, too.
However, unless you have the skills and aptitude for doing this technical work, lots of free time, and lots and lots of patience, I’d also strongly recommend sending them to a service like the one bsd has linked to. When you add up the cost of the hardware and software you’ll need, plus a reasonable hourly rate for your own time, you’ll probably find that even at 59 cents per slide, the service is a better deal.
Second, no matter what you do, DO NOT discard the slides on the assumption that now you have the images in a permanent (digital) form. In fact, properly stored, the slides may have a longer archival life than any digital storage medium you can use. People seem to think that digital media are more permanent than paper or film, but this is not absolutely true.
The main problem with digital media is the rapid pace of changing technical standards. Ten years ago almost every computer had a 5.25-inch floppy drive. These days many new machines don’t even have a 3.5-inch drive. And the vast array of memory cards and sticks that have proliferated with digital cameras are almost sure to be unreadable in another ten or twenty years. And with no reader, your grandchildren will have no way of knowing what priceless memories are trapped on a 30-year-old memory stick they find in your desk drawer while they’re looking for your will. (Hell, they may not even know what the thing is.) Likewise, don’t assume that a CD or DVD will be playable 20+ years from now.
Whereas you can just glance at your parents’ slides with your own eye and tell that there’s something interesting there.
Unfortunately, the best archival method of preserving color transparencies or negs is to have color separations made on B&W film, a process that is more expensive than most people are willing to bear for ordinary snapshots. But proper storage, at the proper temp and humidity, and in good, acid-free archive-quality sleeves and boxes, will ensure that they last as long as possible. IIRC, Kodachrome is the most durable of transparency emulsions, with Ektachrome somewhat less stable. I haven’t looked, but I’m sure that there are numerous resources on the Web on archival storage of film.
Good luck.