One idea about restricting the net would be to "post-police".
Tell her that she has access to all of the net, but that you'll check the logs from time to time and check what sites she's visited, and if you find any thing you don't think is appropriate discuss it.
This way you'll get alot of subjects to discuss
Before letting her out on the net give her a crash course on bad sites, what to avoid and what to close immediatly if she accidently strolls into the wrong place.
And install a pop-up stopper!!!
