You have justification being confused, because manufacturers of scanners, printers and software for them (even Photoshop has confused its share of users) do not (at least did not) adhere to a strict, or even sensible, convention on *pi. PPI can only mean pixels per inch, while dpi can be dots per inch or droplets per inch. PPI or DPI applied to an existing digital image is only a label telling the printer how to print the image a 600x1200 pixel image with a 300 ppi tag means "print at 2 inches by 4 inches, while the very same image file with a 72 PPI tag would be saying to the printer " make me 8.3" by 16.6"
When you are scanning, technically (at least unambiguous) is "samples per inch". Epson is using dpi as dots per inch. They are asking you to choose how many pixels to create for each inch of original artwork or photos in your case in the output scan file. ( Be aware that the scanner has a "physical limit" to its capabilities and it is usually way less than the specs for the product say. The higher and higher numbers are just the scanner offering to take the raw scan data and interpolate them for you. This scanner may say it'll scan at 4800 "dpi" but most folks will say it is not worth scanning much above perhaps 1600 "dpi", around its real physical limit!) If they are good quality prints, you might want to scan at up to 600 "dpi" (there's probably not much more detail in them that would warrant going higher).
So if you have a 3" x 2" photo setting the resolution of the scanner to 600 will give you a file of 1800 x 1200 pixels. This will resemble a digital image from a 2.2 MP camera. If you want to make significant enlargements from this 3x2 old photo, you could scan at higher resolution, say 1200 "dpi" and learn some post-processing tricks to "enhance/restore" them but don't expect to go much bigger than the original. If you had the negatives, however, you could scan them at even higher resolution and expect to be able to make bigger enlargements - the limiting factor in your case right now is the quality of the positive print.
Hope that gets you started
Andy