RULE 1.080 SERVICE OF PLEADINGS AND PAPERS
(d) Filing. All original papers shall be filed with the court either before service or immediately thereafter. If the original of any bond or other paper is not placed in the court file, a certified copy shall be so placed by the clerk.
You should read the Rules of Civil Procedure. You should read them very quickly so you understand what the process is, then read them again. Once you are served, you have a very limited time to respond or you will have a default judgement granted against you. There are a few good lawyers in FL,and a lot of bad ones. You need to find a lawyer or start a lot of research.
The point above is an excellent one. But the key idea is to read the Rules as to your jurisdiction.
In many places, parties are required to serve pleadings, motions, applications for orders, hearing notices and other official papers BEFORE they are filed. But when this is the rule it typically applies only to those filings after the original petition or complaint. Generally, that very first filing is done in advance of service and then defendants are service a summons or citation (depends upon the state).
One someone has been served with the summons and becomes a party to a suit, then different rules apply. And in many places the subsequent filings have to be served first. Even so, the requisites of service are much less stringent after someone is made a party by being served the original summons or citation. In many places, subsequent service can be by certified mail, by facsimile, and even in a few places by regular mail or e-mail.
In many jurisdictions, the subsequent filings are required to include a certificate or affidavit of service attesting that all other parties have been served, giving the address and manner of service, etc. Thus, one has to serve first in order to file these subsequent papers. As a practical matter, many attorneys will prepare the filing and the additional service copies and will drop both the filing and the service copies in the mail OR will deliver the filed copy to the courthouse and might stop by the post office afterwards. As long as the other parties get a timely copy, no one is going to make a big fuss about this.
Key idea though is to know and understand the rules. Also, while taking exceptional care to follow the rules, avoid getting too caught up in trying to cry foul when your adversaries are breaking the rules. Unless you are actually prejudiced by the violation, the court isn't going to be very interested.