It's important to get L3 Farming as soon as possible. As already mentioned, don't increase your population too fast; in fact, I avoid having any kids at all until the supply of food is assured. My strategy is:
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Go first of all for L2 building so you can build the dam and get crops. Then go for L2 science to gain tech points faster. After that, I go straight for L3 farming. Being able to access the coconuts is no big deal as they're not worth much food and the farmers tend to go for them first rather than fish (when available) or pick crops. I reserve it only for emergencies, if my tribe has no more food available. Usually I don't get it until I'm ready to buy L3.

I put everyone I can on research as much as possible. There's no point in builders working on the hut or repairing the love shack, for instance, since they are not yet needed. When food stocks become high enough (I work on over ~500) I'll set the farmer to research. I'll do the same when the crop field is empty. It's important to remember, though, to reset the farmer back to farming when food stocks drop or crops become available, particularly if you won't be able to check the game for a few hours.

As also mentioned, keep an eye open for mushrooms and collectibles, as they can be very useful in increasing food stocks or tech points.

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To err is human; to arr is pirate.