How to sset up that all new couldnt post straight to the site, before this admin should review his post and after this approve it?
Make sure you set everyone to "Contributor." Their completed post will require an admin to review and ultimately publish.
Do you have multi author site.?if yes then the above said solution can solve your problem properly. The only problem with this type of solution is , it does not allow contributors to upload pictures.
Right! Simply make new users with the role "contributor". This will allow them to submit for review. If you don't want user and just want guest posts then try using this plugin: http://wordpress.org/extend/plugins/wordpress-guest-post/