Brig and Brigantine are different vessels -- different rigging. From the little I understand, a brig is two-masted and square-rigged.
The HMS Beagle started life as a brig, but was converted to a survey ship (either a barque or sloop-brig -- I'm not sure which, but it wasn't a typical brig.
While I don't have a source on-hand, I recall reading that a typical brig's crew was the size mentioned in your first post (i.e. 12-16). It included the captain, first mate, sometimes a second mate, a cook and crew. But I know you're looking for British Naval Brig; the crew complement I'm talking about would be for a merchant brig.
Sorry I can't be more helpful, but basically just wanted to alert you that the Beagle is unlikely to be a good model in terms of crew complement given its specific survey role.