Would I serve my husband with the original copy of the divorce papers or make a copy and send him that?

You will serve a copy. You keep the original. Attorneys typically use a process server to get the paperwork served. If you serve, then you have to serve all the papers filed with the court, other documents received from the court after filing and a blank response. I suggest you use a process server or a 3rd party to get papers served. After the service, you have to file proof of service with the court.

File your original petition for divorce with an attached proof of service with the court and depending on your court's requirements one or more copies.  Serve your husband with one of the conformed copies.  Conformed copy means a copy with the court-stamped case number and filing date.