One property you can start to filter by is IsCatalog. Another one you can use is Hidden, although you are likely to use this on your own lists.
/_api/Web/Lists/?$filter=IsCatalog eq false
/_api/Web/Lists/?$filter=Hidden eq false
Filtering out all lists seems a bit tricky, as for instance the user information list doesn't seem to have much information to filter by, except BaseType and ListItemEntityTypeFullName, but that would end up with a huge set of types to filter by (can't filter by
gt as one could use say BaseTemplate 101 (doclib), and 200 (Meetings) while not wanting 112 (User information list)).
But perhaps another hack can be used, at least to narrow it down a little bit more, as it turns out User information list is located in
_catalogs, despite not being flagged as IsCatalog. So we could filter out all those lists, like this:
and IsCatalog eq false