The permissions seem complicated at first but once you realise how they work, it's very easy.
Essentially Default means no or not set, Allow means yes and Deny means Never.
Permissions are cumulative so just keep adding members to each group with the permissions you want to grant them.
So set your basic permissions for the registered user group.
Then any additional groups just set the permissions which are different and their total permission set will be the combination of all groups.
Node permissions have one other thing called Revoke.
You can use that for example to remove posting permissions for a particular group from one node.