Which zone is Fire Island and what type of plants would grow there? Would roses, particularly English roses and clematis be possible? Thank you.

I'm not 100% certain but I believe Fire Island would be considered zone 7 now like NYC.

Whether or not clematis and/or English roses would be suitable would most likely depend on how close your garden would be to the water. If you got a lot of salt spray I doubt either would be happy.

Other than issues with salt water you should be able to grow a wide variety of plants. It all depends on how much sun your garden will get.

You must select plants that are somewhat salt tolerant. With fogs, mists off the water and just the soil itself might have a certain amount of salt in it.
Is your place in an area that saw overwash from Irene or Superstorm Sandy? This would impact your planting's as well.
You can research salt tolerant plants on the internet.

Dont forget about the other huge issue on the Island besides salt water is the amount of deer that roam freely. I would check out the nursery on the Island so you dont have to carry all the plants on the ferry..