Photograph before you read
Take a clear, well-lit photo of every page before you settle in to read anything. This does two things at once. It preserves the originals against the next spilled coffee, and it lets you do the slow work from a phone on the couch instead of hunched over the box.
Flat, even light, no flash, the whole page in frame. That is the entire technique. A phone camera in daylight is enough.
Read each letter for who, when, and where
Go letter by letter and pull the same anchors every time: who wrote it, who it was to, who it mentions, when, and where. You are not summarising the letter; you are extracting the facts that connect it to the rest of the family.
Write those down with the letter they came from, so every name keeps its source. A name with no source is a rumour. A name with the letter beside it is evidence.
Connect each letter to the people it is about
Now the box stops being a pile and becomes an archive: each letter attaches to the people it concerns, so when you open a relative you see every letter that mentions them. The shoebox becomes searchable.
Keep the letter as the letter. Its words can become searchable text behind the image, but the handwriting stays the handwriting. You are building an index over your originals, not replacing them with a tidy retyping that loses the hand.
Know what done looks like
Done is not a finished book. Done, for the box, is that every letter is photographed, read for its anchors, and connected to a person, with its source intact. From there a book is a choice you can make any time, because the hard part, the understanding, is already done.