Is there any way to restrict new members to certain parts of the forum until they've made a set amount of posts or will I have to set up a newbie group and do it manually?

Yes it is .
Create a new group and make what you want at him.

Now create a new sub-forum and do something like that : http://iceimg.com/i/b7/0a/53f8b01c69.png

Ok , now press the Save Button and will look like that : http://iceimg.com/i/8f/5f/f4ab9018b2.png

Press Advanced mode, after that , Write topics or messages : ALL , now at View the forum mark your group and it is done

Cheers, I'll give that a go and see if it helps.

It works , I use this in my forum and don't have any problem.