If I’m currently separated and need to file a Chapter 7, should I file the divorce papers first?

This is a really broad question.  The answer could vary on a huge number of factors.  The decision to file depends on the amount of your current debt, amount of current resources, and the type of bankruptcy that you want to file.  Many people wait until after a divorce because they don't want their ex's spouse's income/resources to be included in the means tests.  Others file before and during because they want debts discharged before they are divided in the divorce.... so that everyone will know exactly what will need to be paid after the divorce.   If you are in an abusive situation, then safety should come first and you would need to focus on the divorce first and worry about the money issues later.

So, much of your answer depends on your situation and what you want to accomplish.  You really need to visit with a bankruptcy attorney and a family law attorney.  More and more attorneys are actually developing practices in both areas because of the overlap in bankruptcy and divorce issues.  If you can't get a combo attorney, put a little time in visiting with one of each type of attorney.  Many will offer a free consultation so that you can get a better feel of what will be best for the facts of your case.  Some bankruptcy attorneys even offer online consultations to get you started.