I'm sure many of us have encountered the original version of this problem in different environments. I do not know how many of us included a watch in the three things to take. Let’s see how I have answered that question, which has quite a potential of being answered pretty weirdly, through the perspective of a watch enthusiasts.
We can start with the question of what we are going to do with a watch in a deserted island. I think, knowing about the date would be more important than knowing the time in such situation. For this reason, a watch with a "perpetual calendar" complication would probably be my first choice. In the current collections of many important brands, it is possible to come across models with the Perpetual Calendar feature. But if you consider the fact that the environment is a deserted island, Audemars Piguet's Royal Oak Perpetual Calendar is one step ahead due to its metal bracelet option. This complication, which is usually presented with a leather strap watch, comes with a stainless steel bracelet with the REF. # 26574 ST.OO.1220ST.01 version. The Royal Oak Perpetual Calendar, which also has a week indicator and moon phase feature, allows you to keep track of the year without any extra adjustment. Self-winding movement also prevents the possibility of the power reserve being depleted -as long as you wear it.
We should not forget the fact that we have to prepare an environment that we can live in, though it will be in a deserted island. It may not sound that important but you have to have a watch where you call “home”. What I have in mind is the Jaeger LeCoultre Atmos desk clock, which produces its own power by using the temperature changes. Although it does not have any complications, I can say that it is a great option for the deserted island use because it will not have any energy problems. Of course, you need to be careful not to drop it while cleaning.
If we do not consider the tide, we may end up having pretty bad problems like waking up in the sea. Therefore, we better take a watch with tide indication feature. Oris Provider Pointer Moon would be a great choice in this regard.
In fact, all these problems can be solved with a Casio Protrek and a few spare batteries, but I do not think we should give up our mechanical watches wherever we are.