Badges are not available yet, since many of the websites features are still in development.
Basic is for everyone.
Innapropriate profile badges are for people who have been reported by others many times in the past. Try to avoid them. The admins will keep an eye on them.
Members will be those who support the site through subscriptions. (More details when those features become available.)
A Gold membership gives you this badge as a thank you for your support. (Again not launched yet.)