Tranfer photos & files from one computer to another

Here's a good opportunity to buy an external hard drive. My son took an old hard drive out of a laptop several years ago, put it in a hard shell to protect it, and I've been using it for backing up everything ever since. I've got virtually every thing I've ever created, done, and needed on that one hard drive, that goes all the way back to the old 8088 processor 5 1/4 floppy disk, green screen days. (Some of those old files ... I don't even have the application program any more). The drive still has unbelievable space left.