Message Groups is developed to organize conversations in Messages app. It provides an ability to divide your conversations into categories just like your wish. The possibilities are endless.
By default Message Groups creates list of default groups for you, by name they are All, All Groups, Favorites and Unknown. This provides a flexibility for you to switch between different list of conversations easily.
Also Message Groups has an ability to set 'Password' protection (requires TouchID) to newly creating groups. This provides excellent flexibility to you protecting certain conversations being visible to others.
Message Groups also supports 'Hide Conversations in Defaults Groups'. This lets you hide your primary or most important conversations in default system groups such as All, All Groups, Favorites & Unknown. Please note that this is a group level feature and when this is enabled all the conversations of that group are completely hidden in system groups. Removing that group will not delete the conversations from Messages app.
What else do you want? Drop a note if you need more features.