Shelter is by far the most important initial consideration. Since you are stranded there anyway, you will have the opportunity to move your camp.
Since you specify a tropical island, you want shelter from the sun more than anything else. You won't freeze to death in the tropics if you aren't on a mountain top.
So in order of importance based on time before it becomes critical:
1) find shelter from the sun (that's going to be your strongest and most consistent element you need to get out of.
2) find a place to shelter you from wind and rain.
3) figure out clothing (remember the sun?)
4) find a source of fresh water (rain ketching is good but inconsistent out of the rainy seasons)
6) nutrients - you won't starve from lack of proper nutrition, but you will weaken over longer periods of time (measured in months and years) This is not an emergency survival need, this is a long term health need.
7) medicine - I am placing this dead last because you either have your meds or you do not and there is nothing you can do about this.