Start by adding the people you're shopping for, or a sub-group such as a branch of the family.
Your list is saved only on this device, in this browser. Use ⋯ → Back up now and then.
Tap a group to pick everyone in it, then untick anyone who shouldn't get it. The price is counted once.
Tick several groups, or link to someone with the same name, and they share one list everywhere.
Closing this keeps things as they are.
Tip: on iPhone, tap Share → Add to Home Screen; on Android, tap ⋮ → Add to Home screen. It then opens like an app. Your list stays on this device only.