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Flax

Flax is a plant that was often farmed in Medieval and Pre-Medieval societies around the world. It was an important resource to many societies for several reasons:

Food

Firstly, its seeds can be turned into a meal or used for linseed oil, a finishing used on wood to protect it from weathering or it can be injested as it too can be edible. The meal produced can be eaten, used as feed for livestock or ground into flour to make bread.

Linen

Perhaps the most useful use of flax was to create linen, a textile. This could be used to make clothing, bedding and pratically anything that cotton can make, flax can make too. A huge feature of linen though is its ability to produce extremely protective armour. By layering pieces of linen, you can create a gambeson, a type of armour used by both rich and poor for its protective value.

String

Because flax is string. Flax is used to make string, even today, by twisting the fibres of the plant together. As you can imagine, string is highly useful for temporarily holding things together. You can also keep twisting the fibres together until you get rope, which can be even more useful if you need larger, heavier objects holding in place, such as a ship or drawbridge.

Other Uses

The same fibres used to make string can instead be used to make canvas, slightly less useful but can be highly valuable with paint on them. It can also be used to make paper, flooring, inks, paints or just be grown as a decorative plant.

Supposedly its specific epithet, usitatissum, means “most useful”. The plant has been cultivated since at least Ancient Egyptian times and has been grown all over Europe and Asia for its numerous uses.

Most of your list is irrelevant. You need the big three and maybe two more things. The first and last thought in your head has to be FARMS, farming is everything, if it it not used on a farm it will not have much use.

Drinkable water

arable land

A robust supply of lumber

Everything else is a product of these three things, or incidental and not really required. Ideally there would some clay and iron deposits as well but these tend to exist everywhere that has the above. Of course you also need crops and a livestock but people tend to bring those with them. Farming is the basis of society it supports everything else and the majority of your population will be farmers. Regular rain will be important if people can't farm they are not going to live there.

water is self explanatory, rivers and ground-water can supply that. Arable land is the basis for food, hunting occurs but it is not a huge focus of society. Wood is the basis for all technology tools, homes, cooking, all are wood resources, even the charcoal used for metalworking is made from wood. the few things that cannot be made of wood are usually made of clay or a metal usually iron or copper. A naturally occurring plant useful for cordage like hemp or linen may be helpful, but people will farm these plants as well.

Some other things would be nice to have but they are by no means necessary, fishable waters, source of salt (either mines or bays), good harbors, limestone, these are nice but my no means necessary.

If you want to get an idea of what life would be like There is a great BBC series available on line called, tales of the green valley that is about a group of experimental archeologists and historians recreating a Stuart farm and living there for a year. The later series about a tudor era farm is even better. It can give you a great idea of what is really needed for civilization of that time. A later program by the same people is about building a castle using all period techniques, secrets of the castle) and you will notice that even there the only other resource they use is occasionally lead and chalk. Shapeable stone like granite or sandstone are nice but places with arable land tend to have those. Arable land needs a mineral source which is usually nearby mountains.

Tin, coal, precious metals, gems, and marble are more or less useless in such a society, or so hard to use or get that they are only used for expensive showy non-essential uses. They may be used if available but they are by no means necessary.

Arguably, the most imporant resource was land.

Arable land provided a way for the local lords to gain economic power: by providing protection for the local populace in exchange for food and good that they produced. Whilst the food itsef is not likely to make them a fortune, they would not be able to make the money if they and their men were starved half to death constantly. Land was often given to wealth lords or knights by the ruler as a reward for various things.

Even non-arable land would have some uses, such as being ideal to build upon as you would not need to worry about losing out on useful, farmable land. You might also be able to house animals on there, assuming you have some way of feeding them.

Additionally, hills and mountains would be highly valued for their defensibility. Castles and fortresses were often built on them where possible in order to have a staging point and fortified poition in case of an attack. This also allows for you to defend other resources that you own, such as forrests, quarries, rivers etc.

Access to coastlines and large rivers was also extremely important. If you have access to the sea, not only do you have a source of fish for your local population, you can create docks and ports to allow for trade with other regions or even other nations. Alternatively, having sea access meant you could defend your country from invasions via ships, intercepting them before they landed.

Alternatively, you could argue that the most important resource was people. Without the backs of labourers, the hands of artisans and the swords of soliders, the lords, and indeed countries, would not be able to gain the wealth and influence that they had and nothing would ever get done.

Good points all and valid.

Civilisations of the past have failed when they outgrew their local resources, usually wood in the limit as it is impractical to transport over large distances.

However you show a medieval island that is small if the features that look like mountains are mountains.

So the most important requirement is a human gene pool. There are various theories and numbers that are bandied about, but in the end you need to have enough people and enough land to feed them. A small island nation will not survive indefinitely with a fenced population.