I am getting married to a man that owes back taxes not sure how I should file married seperate or Single? Should I file a injured spouse claim form as well?

If you are referring to tax year 2018, then if you get married in 2018 and live together at any time during the last six months of the year then you can only file your 2018 tax return as either Married Filing Jointly or Married Filing Separately.  If you file as MFJ then you should complete a Form 8379 Injured Spouse Allocation so your portion of any federal tax refund will not be seized for the back taxes owed.

If you were not married as of 12/31/2017 then you would only file as Single on the current 2017 tax return, unless you have a qualified person as a dependent and you provided over one-half the cost to maintain your household then you could file as Head of Household.