I will try to explain the chain of custody thing. The chain of custody relates to how evidence is kept as to a certain extent as to how the way evidence is collected. The chain of evidence means an identifiable person must always have the physical custody of a piece of evidence. In practice, this means that a diver that collects the evidence will take charge of a piece of evidence, document its collection, and hand it over to an police investigator or evidence clerk for storage in a secure place. These transactions, and every succeeding transaction between the collection of the evidence and its appearance in court, should be completely documented chronologically in order to withstand legal challenges to the authenticity of the evidence.
Documentation should include the conditions under which the evidence is gathered, the identity of all evidence handlers, duration of evidence custody, security conditions while handling or storing the evidence, and the manner in which evidence is transferred to subsequent custodians each time such a transfer occurs (along with the signatures of persons involved at each step).
For example, suppose a diver finds a handgun. Measurements are taken as well a photographs to document the location. Commonly a metal rod could be driven into the river bottom to further document the location. The gun should be placed in a container that also holds the water in which it is found. I like using a PVC pipe with test caps on the end to keep the gun in. An evidence tag and tamper proof seals are put onto the container. Initials of the finder should be scribed onto the gun and a evidence form kept showing the name and date of each person the gun is given to, the description of the evidence, etc..
If I find a gun diving I do all the above and submit it to the crime lab for analysis. A receipt is kept of each person whose hands the gun goes through. After getting the gun back from the lab I sign for it and then place it into my evidence locker and maintain possession of it up to the time it is introduced into evidence at trail. I then file the certificate of analysis with the clerk of the court where the trail is heard. (Your state requirements may vary). This is a brief example of chain of evidence.
The problem is that you can still maintain a proper chain of evidence and still manage to screw up a criminal case big time by improper evidence handling proceedures if you are not trained to handle evidence, especially evidence found in the water. A gun could hold latent prints underwater for possibly five days. A fresh gun should be handled in a manner that will enable the prints to be collected and not smudged. A person may try to work the action of the gun to determine if it is loaded. Failure to properly document the condition of a gun is very bad mojo. Just because you can document the chain of possession of evidence does not mean that it will be admissible if it was contaminated somehow while it was collected or improperly stored.
For example, if it is a revolver the gun needs to marked which chamber is aligned with the hammer and a sketch made of the cylinder indicating which cylinder is empty, loaded, or has a fired casing in it. Document whether the cylinder rotates clockwise or counterclockwise, etc.Failure to do this could jeapordize a court case.
In the example of the gun found in water it is necessary to package it with the water in which it is found. Even exposing it in air for just a short time could cause flash rust to occur which could jeopardize microscopic analysis of the gun.
Other evidence such as clothing could be destroyed if stored wet and not air dried before packaging. Some evidence is best stored in plastic bags. Other evidence needs to be stored in paper bags to avoid damage to the evidence.
This is just a very short description of some problems that can happen with evidence. The defense attorney will not be doing his job if he does not force you to show that you did everything correctly and the evidence was not mishandled in a matter that the evidence was contaminated, adulterated or manipulated in some way. If they can show that the evidence you worked hard to find was improperly handled it may not be made admissible during trail.
If you don't have proper training and you go grabbing stuff out of the water and screw it up a lawyer is going to make you feel like a complete ass. I have been testifying in court for 30 years and don't like defense attorneys as a rule. I like them even less when they point out a screw up I did and I have done my share. Good training and skills will keep you from being in the hot seat in court and you will look like a porfessional instead of a fool if you do it right.
Most dive teams started the way you have. That is how I started out, with a few guys with an interest in diving. As time went on we became more professional and got proper training. Now we have thirty divers and a bunch of very nice gear including side-scan sonar.
I have various PSD certs in underwater criminal investigations and that is they key to collecting and handling evidence underwater. Setting up and funding a dive team as well as the equipment you need is a whole different headache that I will let someone else address. Good luck !