Good advice above, but also think about the future. Will your kid's kids like the photos, how about their grandchildren and future generations? How do you want them to be depicted? You know that even relatives do not want to look at hundreds of photos, nobody does, so pick the ones that are actually good photos or are representative of periods of development and what their talents are (when they are older and have a talent or interest).
MOST IMPORTANT: print them out, and better yet assemble printed albums that each can take with them as they leave the fold. At least one album might survive who knows how many years or even centuries. You can back up digital stuff a million times but it will not survive. People will be lazy and won't copy it over to each new storage technology, something that could change dozens of times. An album is hard to throw away and will survive even if neglected and thrown in the attic where it will eventually be discovered by someone who will find it interesting.
Add identifications and comments that you feel will stand the test of time. Make sure your name is there, and photos of the parents and other relatives so people can put this all together in 100 years and know who is who in the family history.
If you have a drawer full of old photos, scan them and print them out in album form as well. Do this now before something happens.
Make sure they know that carrying on the tradition is important and hope that at least one of them does.
I followed my own advice and when my kids had to evacuate due to a fire, they grabbed the dog and cat and the albums.
My albums were assembled and printed out via Aperture. Terrific. Sorry All-So-Connected Apple hot shots: Quitting Aperture was a nasty thing to do. Be thin and streaming while twittering if you must, but leave good stuff alone.