I'm afraid I disagree with several of roldwol's above points, though in fairness castaways is a game with lots of methods to success.
First thing to remember about the game, is that jobs are flexible, the more people assigned to one job, the faster you get things done, but also not all jobs are needed all the time. This is what makes castaways unique, playing adaptively.
Next thing to remember is that everyone does not have one job but two. Thus a carpenter will work as a wood cutter when there are no logs to cut into lumber, a baker will work as a peasant when there is no flour etc. Thus, by assigning jobs carefully you can make one person do extra work, for instance I don't find it's necessary to have a dedicated woodcutter until later in the game, sinse the carpenter will do the job too, ditto with miner smitth and metallurgist, (I usually asign just one smith and one metallurgist).
The other thing is peasants. peasants actually do the most work and the most diverse range of work, but this means you need lots of them, sinse they will be doing different tasks, for instance, once you build a mill and a bakery, they will start grinding flour, and once you build a textile mill they will start spinning cloth. so, always! try to have betwene a third and a half of your population peasants, even if you temporarily need to take people off resource collection due to people being ill. this is also why it's important to have a big population.
As far as building placement goes, your right in assigning building close together, however also remember that firstly the goblins come from the top and sides of the map, so you will want to build in the bottom center, also if you are close to the sea building the boat to end the mission will be far easier.
so at the start, the first thing you need built is an inn and a storehouse, thus assign everyone as builders so as to get the building done quickly. When you have an inn, assign a cook, and you can start serving meals, also assign fishermen or hunters. Fishermen give meat at a constant wrate, while hunters vary according to the forest level but also provide pelts, thus can give a lot at the start of the game, so pick your poison (I usually go for one of each which will serve for a long time).
Next, build your sawmill and quarry. At the start, you will just need one stone mason and one carpenter, because the carpenter will double as a woodcutter, also remember to make most of your population into builders while building then turn them back to peasants afterwards.
You only need a doctor when someone is injured, indeed sinse a doctor's secondary job is taylor, you don't want a doctor most of the time, however it is usefull to have a hospital to build one.
food wise, you don't actually need so many farms at all, and certainly not so many farmers, sinse one farm provides more food than one farmer can harvest. Vegitables are the easiest food to produce sinse the farmer can just harvest them with no preparation, so I'd recommend building a vegitable farm before starting on houses and getting your population up.
now, is when you need to diversify. build a mine because mining takes a long time, then another house, then a smithy, then another house, then the makings of bread production.
Once you have a smithy and a mine, you should have some spare people, and can assign a smith and a metallurgist. As soon as you have weapons made, start assigning soldiers to train as knights. Knights are hugely more effective than soldiers, and seven or eight knights can keep the goblins in check nicely, especially if you help them building guard towers towards the edges of the map.
After thisyou can concentrate on growing your population and getting cloth and wine production up. Just remember in castsaways people count more than buildings, so if you need more food harvested, it's better to assign extra farmers than build more farms (go on a ratio of 2.5 farmers per farm and you should be about right)
Also keep an eye on all your stocks and assign more people if they start dropping.Generally I finish mission 1 with a population of about 40 or so, ---- though once for a laugh i got my population up to around 100, and once when i was really trying hard I finished with a population of 24, though I believe it would be possible with less if you were pushing.
Just always always always! remember the game is adaptable. you win in castaways by adpting to your current situation and projects, not by making a set plan and sticking to it to the bitter end. Make sure you have no people standing around idle, and your sure to get through.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)