I'm very new to ArcGIS (and GIS in general), and I'd like to create a map of the Caribbean region colour coded for certain indicators. I need each island to be a different colour depending on that indicator. Would anyone be able to direct me towards resources that might help me with this?
Esri Training would be a good starting point for an introduction to ArcGIS and GIS in general. There are a lot of free courses available there. For example: Getting Started with GIS.
More specific to the map you want to create, you might search for guides and tutorials on creating choropleth maps. A few examples:
Choropleth map - GIS Wiki | The GIS Encyclopedia
Creating a Basic Choropleth Map in ArcMap
Choropleth Mapping in ArcMap - YouTube
Basically what you'll have to do is: