Read first, or watch first?
Read first, and then be selective about what you watch. The 1996 miniseries is the one to pick if you want an adaptation of the book — it is the only version that has ever filmed Laputa or the Houyhnhnms, Danson is genuinely good, and it does not flinch at the fire in Lilliput. But it rewrites the ending into a reunion, and if a family watches it first they will read the last chapters expecting a homecoming that is not coming. The 1939 Fleischer cartoon is a lovely thing to put on with a younger sibling and is not really this book at all; the Harryhausen is worth it for the effects and the Herrmann score. Skip the Jack Black unless somebody specifically wants it, and if you do watch it, watch it after — the joke only works if you know what it is stepping on. One practical note: most people who say they have read Gulliver's Travels have read Lilliput, because that is the part the films and the children's editions keep. The distance between that and Part IV is the whole point of the book.