Welcome to the Workshop community @GraemeB. I'd be happy to answer your question on what screws to use when fixing timber to metal.
It would be great to know what thickness your steel runners are on the trailer. I can advise using Buildex 8-18 x 30mm-Climacoat Countersunk Ribbed Head Metal Tek Screws, as they would be sufficient to hold the 15mm marine plywood. Please be aware when installing that there is not any wiring or functional trailer parts which will be impacted by the placement of the screws.
You can seal the marine plywood with an exterior varnish or exterior paint. Due to the nature of trailers, wear will occur on those products and degrade them after some time. An option to consider would be fixing Galvabond sheet over the top of the marine plywood as this would protect it from damage.
If you have further questions or need assistance with these products, please let me know.