The best way to store old pictures is by putting them in frames. You can also buy a huge photo album to keep them safe. You should store the pictures in good condition, because sometimes they remind us of who we are, and where we are from.
Flash drive. Not on your computer because it can be lost. And if you keep in in picture form they can get ruined. I suggest keep them all on a flash drive and in picture form that way you have 2 copies
Store them in acid free photo storage boxes or in albums with acid free sleeves. They are available in most craft stores and photo supply stores. Make copies of the pictures you want to display and store the originals if they are very important to you.. If you want to display the originals, frames with glass are better than the ones with plastic protective covers and hang them where they will not be in sunlight.
Real photographs should be stored flat and in a dry but not hot place. They will last well over 100 years. Digital photos unless stored on archival discs will loss their integrity within 3-5 years and be lost forever. Now if you store them on museum quality discs, be sure you also save the computer and all the rest of the equipment and programs that allows you to view the photos because 20 years from now the computers then in use and the programs will not recognize the old photos. And if you print them out they must be on Kodak quality photo paper, otherwise they will fade within a few years. The new and wonderful is not always so new and wonderful.
Keeping them in a frame is a good idea. I like to buy a picture album and decorate the inside with the pictures. You know, stickers and stuff. After that you could put it in the living room or something for others to see...
DO NOT FRAME THEM!!! Photos need to be stored in acid free boxes in acid free sleeves. Prints behind glass can get damp and glue themselves to the glass. There are several places on the Internet that sells these supplies. I have been a professional photographer and restorer for 30 years and I have seen so many mistakes throughout that career. If you want to frame prints make copies and display the copies and put away the originals. Especially old photos that can never be replaced. Photos exposed to ssunlight, infrared and ultraviolet rays with continue to fade and ruin over time. Having them digitized is one way, but them what media product is going to be around years from now?