Say 100-200 people, enough earth to crow crops, water and energy. Mimic the food recycle system on earth and you will have people who could colonise a planet because they have been colonising a ship.
My wife is an author who studied out generational ships for a series of fiction books. We've discussed it quite a few times. While a very small crew of perhaps 80-100 people could run the ship during transit, they would be insufficient to establish a colony. A better number is around 10,000 to 20,000 people, but only after habitable planets are discovered and colonization plans are developed.
There are many major barriers for humans to travel between stars, among the two biggest are keeping people alive during transit and colonizing the planet on arrival.
Cryogenics is popular both in fiction and real-world research because of the first barrier. The trip will take a long time and space is cold. I mentioned it on the last page of the discussion thread, but it bears repeating. If people can be frozen for the trip there is no energy needed; deep space is very near absolute zero, generally only single-digit kelvin temperatures. However, if people need to be up and awake and doing living things their living areas need to be heated. Keeping it heated means constantly spending precious energy to compensate for all the heat being leaked out to space. Keeping people active during the trip means solutions to all the problems of food and water and recycling, all of which require energy. For stupid reasons I always imagine this as people having a little pop-up turkey thermometer as part of the cryogenics process, they're ready when the button pops out. :-) Whatever way you do it, you need to make sure the crew have all the skills they need to establish the colony when they arrive.
Once they get there they need to set up the colony, the second barrier. While a few hundred people could potentially handle the baby-making aspects, the bigger problem is lost skills and lost knowledge. There are many roles that will need to be passed along. If you've got a hundred person generational ship the only skills that will survive are the ability to maintain the ship (hopefully) and the ability to raise children. The population base is not large enough to retain a working knowledge of other skills. Some of them could be kept in books but without real working knowledge there wouldn't be a way to preserve it. The small crew would arrive after many generations, pull out books in a language they were taught to preserve, and find instructions about assembling habitations, analyzing their new home's features, engaging in physics, chemistry, biology, architecture, construction, sanitation, and on and on. You also need culture; artists, musicians, sculptors, and so on. When the ship arrives they need several thousand people with experience in several hundred fields who can immediately get to work.
There many other issues than those two, but generational ships are generally considered impractical if the goal is establishing a settlement. They might make sense for other purposes, such as a genetic ark or for certain types of research, but the costs of keeping people up and running for several generations are enormous.
On the ethics topic, what do you do if the next generation revolts and wants to change course? Is it their right to turn around and accelerate back towards earth instead of finishing the journey? (assuming there's enough fuel to do so) What kind of government should rule over them? Typically on a dangerous vessel, the right to choosing government is suspended and a singular captain is chosen to be responsible for everyone's fate. Should the crew have a democratic right to choose their own captain? And should the captain have the ability to change the course?
These are all among the reasons against generational ships, and they all strongly favor cryogenic solutions. The frozen crew is the original group who willingly made their decision. Presumably they will have been like-minded enough to establish rules for colonization, including governance at their new home.
Since the crew effectively has no time pass when they are frozen, they keep all the other benefits above for establishing the colony.
A short-term ship where only a single generation is needed --- the original launch generation raises children who will settle the colony --- has the least problems with those issues. If the trip can be made in 50 years or so it can work out. Every new generation adds more complexity to the issue.