So let’s say in the distant future, it is decided by the New World Order/a group of wealthy individuals/mad scientists that the human race needs to expand outside of the solar system. Space travel has advanced to enough of a degree that while faster than light travel isn’t possible, the speed of the ship is sufficient so that from the frame of reference of those on the ship a single generation will pass even if hundreds or thousands of years may pass on Earth. A planet of similar gravity, atmosphere and temperature range is found, though the biology of what may live on it won’t be known until arrival.
Assuming some form of suspended animation isn’t utilized, it’ll be the children of the original travelers who colonize this planet. Let’s also assume that there are frozen sperm and ova on the ship for genetic diversity, so a huge number of people for that purpose aren’t needed. Bodies and brains are needed, not DNA.
Now, how many people will be needed for the initial departure? How many children should they have while traveling in order to establish this colony? What skills and professions will need to be represented? What can be left to reading and computer simulations and what needs the voice of personal experience? Keep in mind that the colonists will be raised in space. They have access to some portion of the ship set aside for growing plants and animals for food, but will have never touched a planet before they have the responsibility of colonizing handed to them.
In Alastair Reynold’s Chasm City he has about 150 crew on his “generation ships.” This is apparently enough for subsequent generations to continue running the ship itself but he also has 1000 “sleepers” for the actual colonisation which violates the rules of your OP.
The requirements for a long-term gene pool are unclear, but the case of Tasmania (an original population of a few thousand isolated for a few hundred centuries) sets an upper limit for the minimum.
I would advocate that rather then a convential spaceship a moving version of the,was it O’neil habitat?
ie .a large tube rotating on its axis(To simulate gravity) with the inside of the tube landscaped ,be utilised for the colonists to make their lives a little more bearable .
I do have a caveat on the gravity simulating rotation as I’ve heard that it causes problems with the inner ear and balance,but hopefully that could be overcome.
I would also suggest Earth sends a continuous stream of media to the habitat so that they feel less alone AND are kept on track as to what is normal behaviour(Just in case they start a religion that relies on cutting peoples hearts out to keep the main reactor supplying energy to the ship).
I realise that if they do go off of the rails this communication from the home world wont be able to give them orders or threaten them but it MIGHT just tip the balance when sanity might be in a minority amongst the voyagers.
I also realise that the further away they get from the Solar System the comms from Earth will take an incredibly long time,decades maybe,to reach them but something is always better then nothing.
And my final thought on the matter is that the colonists should constantly be recording scientific data on the space around them and sending back home to keep them busy,give them a sense of purpose plus it may even be useful to those back home.
Used to be member of the British Interplanetary Society when I was young.