First what you need to do is change the wiring coming into your trailer. It needs to be a 4 conductor wire, not a 3. The reason for this is that you are risking a shock hazard by not having your trailer properly grounded. You accomplish this by running a cable with 2 hots, neutral and a ground. Your new panel needs to have both a neutral bar and ground bar separated so they are not electrically connected. Next you will need to run a #6 wire from your grounding bar in the panel to the chasis frame of the trailer.
Now as for the size of the service, you will need a 50amp 220v 4 wire cable to service this trailer. Most all units such as yours run off of of this type of service. Now if you were able to provide me with the amperages of all the units running inside your trailer, I can be much more specific.
As for the panel, I would recommend putting Cam Lok panel mounts. All fairs, convention halls etc will use cams as a standard of making the electrical connnections. See pic:
What you would need is Red - Black - White - Green cams. These would surface mount on your Nema 3R electrical panel. Like I said in most cases, they will run feeders to your trailer and with cams already attached, all they do is tie them into your panel and your off and running. If them running cable to your trailer with cams already attached is out of the question, you will need a 4-4 SO cable. This will allow you up to 75amps and if you only needed 50, then that would make up for the voltage drop in the system. Additionally, I would still hook up the panel mount cams and then put cams on your cable for easy install and tear down. See pic:
Now your cable wont exactly look like this, but these are the cams for your cable and it will be one cable not separate feeds.
Now I know this is allot to take in, but if you have any questions or need clarification on anything I stated, please dont hesitate to ask. Have a great night.