There are tactical advantages for the person who files first. The legal document that starts the proceeding is the Petition for Divorce or the Complaint. It also covers certain technical matters and asks the court for anything you might want.
If you and your spouse cannot agree on something (support, visitation, property division, attorney’s fees, court costs, maiden name restored), then you must ask the court for it in the petition or the court cannot give it to you. If the list seems long or includes more than you think are appropriate, think of it as a wish list. If the wording seems strange, remember that it is a formal legal document and much of the wording is required by law. If your spouse has already filed, be sure that your lawyer has a copy of the petition as soon as possible.
The person who files first is the plaintiff or petitioner. The other person is the defendant or respondent and that person must respond to your petition in a formal document known as an answer. The defendant may also want to complain that the plaintiff was at fault. To do so the defendant files a Countercomplaint.
If possible, talk to your spouse about divorce before you file. It is hard to keep open lines of communication if your spouse has been surprised by the sheriff serving divorce papers on him or her at 4:00 A.M. (which is when the sheriff often serves papers).