If you are using Photoshop Elements 9 (or Picassa), there should be a dialog box / window somewhere in the program to enter IPTC information (International Press Telecommunications Council) which is meta-data associated with the image file. IPTC is a standard and will be readable by many programs and will include fields for things like caption, keywords, location, etc. EXIF is a similar form of metadata usually added by the camera to hold information like exposure settings, etc.
Many programs allow you to easily enter IPTC meta data for multiple images at once. For example, in lightroom you can select several images with your mouse and enter the caption "Bob's birthday party, Chicago" all at once. You can also do this with keywords. Using this batch entry of meta-data is very fast.
I believe Apple's iphoto and aperture programs will also perform face-recognition to caption/keyword photos to label people in the pictures. I have not used this functionality so I can't comment on it's effectiveness.
The meta-data is stored as a header in the file, so it's only visible in a browser. If you want a caption to appear on the image itself, you will need to enter it manually with the text tool in PS. If you are good with scripting, you can probably also achieve this with automated actions (photoshop has this, not sure about elements) or with third party tools like ImageMagick and ExifTool.
On Tiff vs JPEG, I would recommend storing the images as high quality JPEGs. The reason most photographers prefer using TIFFs is that if you make a lot of edits to your image (and resave the file as a jpeg multiple times) you can get noticeable degradation. TIFF also supports 16bit images which is important if you do heavy postprocessing but probably unnecessary for snaps. The advantage of JPEGS is that the image files will be much smaller and easier to view especially for non-technical folks. Many professional photographers only shoot in JPEG because their smaller size makes them much easier to work with.
You will probably want to create two versions of the files: (1) A high-res "master" that captures the image at the full (or nearly full) resolution of the scanner. This is the file you should use if you want to print the image. (2) A smaller web sized picture that might be say 600x900 for sending to friends/family.
Also looking for suggestions on how to store the original photos. Some are old (early 1900’s) large and bulky.
I would take them out of frames/albums and store them in archival boxes/envelopes.