Hello SharePoint Experts... Looking for some advice.

In my Document Center I have a central Document Library for corporate Policies, procedures, strategies and forms. (i know forms does not belong here)

The situation i am faced with is that most staff in the office will require edit rights on specific documents somewhere in the document library.

I want to have a view the displays the latest published version only. Drafts remain hidden unless you go directly to the list. Can this be done? is their a better way?

A few things I am trying to avoid:
1. I want to avoid structuring my document shares by departments (Silo thinking). I want all my policies in the same location.
2. I don't want top have to train users to look at version history to view the latest Published document.