Upgrading your field will give you more available seeds! So a level one field will allow you to plant Oranges on the Tropical island and Flax on the Nordland farm. Once you upgrade you will be able to plant Peanuts or Herring, depending on the farm!

For the full list of seeds and when they become available, you can tap the blue information button that appears in the bottom left-hand corner when you select your field.