For your avatars you can just take out the fields in the Registration and Profile files (where the users add their avatar URLs) and just insert them via CP. This prevents users from inserting their own avatars. To have an avatar the users make an avatar request. We've imposed restrictions on what users can submit as an acceptable avatar and only after we allow it we'll upload it for them.
One of the benefits of being a member on our board is that he/she can request a custom avatar or signature and our team will create it for them. It is safe and I can happily tell you that the members love it.