When I add information beside a word in a Bible verse, what bracket should I use? Parentheses or square brackets?
If you are adding just the chapter and verse, you can use either, or set it apart with a dash.
If you are adding notes in your own hand, then it would be more common to use brackets for that (with any quotation, not just biblical). As such you might wish to opt for parentheses for the citation, to be distinct from that. For example:
The wild beasts of the desert shall also meet with the wild beasts of the island, and the satyr shall cry to his fellow; the screech owl ["Lilith" in many translations, "Lamia" in the Latin Vulgate] also shall rest there, and find for herself a place of rest. (Isaiah 34:14 King James Version)