Oh I see, so I need to use the FoF Default Group extension to create a group for new members who I will later move to the regular Member group.
I'm not sure you need the FoF Default Group extension. Otherwise that's the idea.
EDIT : I have an issue, those who can start discussions without approval should be the regular members, and those who can start discussions (all short) should be new members, correct ? Well the permission system forces the can start discussions group to be the same as the can start discussions without approval !
This is not the case. You can allow all members to start discussions. As long as they don't have the permission to start a discussion without approval, of course they need an approval. The ability to start a discussion without approval should therefore be limited to a specific member group (you can call them regular members, later, as clarkwinkelmann specified, you can hide their group status).
I also want those new members to only see part of the forum, is the above compatible with the tag restriction ?
EDIT : seems like I can only allow a tag, so if I wanted new members to only see one tag I would have to block them from seeing all the others and that is a heavy permission setting.
You can apply several tags to each discussion depending on your settings. So you may have a tag "public" to show discussions to everyone and another "semipublic" to show discussions to new members. Discussions without any of the described special tags would be visible only to your elevated (regular) member group.
Take a look at the Solved tag here in this forum. This tag is used in addition to other tags like Support, Feedback or Dev. You could set it up so that discussions tagged with Solved are only visible to registered users or a specific member group. (Of course that doesn't make sense here)