1. A survival guide
2. A botany book about tropical island plants and their properties
3. A machete
4. An Axe
5. A large magnesium strip and striker
6. A shovel
7. A tarpaulin/plastic tent
8. A crossbow and bolts (less likely to break than arrows for a bow)
9. A large supply of medicine
10. A metal bucket/cauldron for cooking and water collecting
Solar panels, lights and a laptop with survival guides on its hard disc would be good, but easily broken and hard to repair. A book is sturdier when it comes to sand and mud.
Rope we can make. Fire we possibly could make, but I reckon that the ease of having a striker is worth a slot. Shovel for digging fish traps, cesspits, ditches, fields and so on. Machete and axe is obvious: machete is an all purpose knife, probably a bit unwieldy for gutting fish, but we don't have enough slots available.
Medicine because it keeps me going.
Crossbow for easier food collecting.
Botany and survival guide for food, shelter and possibly antibiotics.
If I had more slots I'd like a smaller hunting knife, more pans and more waterproof sheeting (shelter for us and firewood). Some blankets, spare clothing including specialist stuff (I'd go dressed in my walking boots, sturdy trousers, mountain jacket and so on, but jumpers for cold people, gloves, waterproof trousers, razors, scissors and so on would be nice too.
Lastly, it'd be quite nice to have a lot of paper and ink. Perhaps that laptop would be a good idea after all.