One of my favorite subgenres of science fiction is the space colony novel. It blends survival fiction with cool science, and lets you have gorgeous scenery instead of just the inside of spaceships. And there are endless cool biological things you can have happen.
It’s also an interesting place to talk about colonialism. Generally you can sidestep the whole issue by having nobody live on the new planet when your characters arrive, but even then you have to ask about the ethics of claiming a planet just because you got there first. Do you have to let anyone else who arrives there share it with you? Is it right to terraform a planet when you haven’t thoroughly studied it in its natural state? If there are people, then it’s a whole other kettle of fish. What kind of characters just waltz into a place and think it’s theirs?
But I’m not going to go into all of it because I could write a whole novel on just these themes (and did). Instead I want to talk about the practical considerations of what you would need to bring on your colony ship. How small can you make it and still have a functioning, independent colony at the end?

The answer is solidly, it depends. How independent does it have to be? Are there going to be trade and occasional visits without outsiders? If you don’t need to bring absolutely everything you’d need for forever, it helps. Next, consider the tech level. Are you aiming at a subsistence level colony, or will you need enough people to found a university to keep up with skills? Do you have robotic labor, or do you need manpower enough to do everything by hand? Finally, how much information do you have? If you’ve visited the planet before, you’ll have an easier time knowing what you’ll need and won’t need to bring quite as much.
So, here are some beginnings of a packing list.
People
How many people does it take to form a functioning colony? This is really two questions. First, you need enough people to avoid inbreeding and genetic problems. Second, you need manpower and expertise enough to run the colony.
If you are never going to have contact with the outside world again, you need at least several hundred people to have enough genetic diversity. A thousand would be better. Keep in mind, though, that you don’t actually need people per se, just genes. If you bring only women and a whole lot of different sperm, you’ve saved a lot of space on your ship and not cut the genetic diversity at all. You can bring all the embryos you’ll need for generations, if you want to. But keep in mind, that requires the colony maintain a high enough tech level. If the freezer ever goes out, there goes your future.
In that group of people, particularly in the first wave if there are successive colony ships, you’ll need a broad array of specialties: engineers, botanists, doctors, teachers, chemists, leaders. The leader and system of government should be chosen before you leave, with a process to amend those decisions in light of conditions on the ground. Mid-landing is just a really bad time to have a revolution.
Plants
If you’re headed to another planet, you’ll need food, and that means plants. In theory, you could eat the alien plantlife. In practice, there’s no reason any of that would be edible to humans. Simply turning a starch around backwards makes it indigestible to us. Or perhaps the planet’s flora accumulates heavy metals or something. Plus, if there’s nobody on a planet, there’s no domesticated plants, with high calorie yields. Do you know how many of the plants you currently eat come from thousands of years of domestication? Spoiler, it’s almost all of them.
Depending on the climate of the planet, you may need to genetically engineer the plants you bring with you to adapt to it. If the soil has different nutrients than Earth’s, you may have to amend the soil or introduce nitrogen-fixing bacteria to it. Did you know Mars’ soil is extremely toxic, thanks to perchlorates? (Mark Watney didn’t.) It would have to be thoroughly rinsed to make it arable.
Animals
You don’t technically have to bring animals. You could plan on everyone being vegan, so long as you bring bacteria that make vitamin B12. But people tend to like having animals around, and eating animal products, so it’s safe to say that unless they were vegan they’d probably find a way to bring animals.
Large animals, though, might be tricky to bring on a spaceship. Goats and chickens would probably be more popular than cows and hogs. Fish and crustaceans could be a good choice in a domed or underground colony, where space is limited.
Information
If you want to keep all the technology that got you to the planet, you’ll need all the knowledge that underlies it, enough to train the next generation. For that, you’ll need computers, which means power and plenty of backup batteries.
If you want a bucolic life, close to the land, you wouldn’t need to bring so much–but you should probably record, on paper, where you came from, or you’ll end up with a Pern situation where eventually nobody knows any of it.
Supplies
It would be impossible to devise a packing list that could ever include everything you’d ever need. So bring a 3D printer, have tools with easily printable/swappable parts, and consider ways to make what you need when you get there. Medicines will be especially crucial. Those with organic components, you’ll need to bring seeds or genetically modified bacteria for. The rest, you’ll need chemical ingredients to synthesize.
Most colonies will want a power supply. Nuclear is a popular option because it can go for quite a long time without refueling, but eventually you’d need to find more radioactive material for it. Solar, wind, and water are other options. Wind and water have the added advantage that a person without much training and limited materials can set up and repair it.
As you can see, founding a colony on another world is a huge undertaking, with a lot that can go wrong. I like imagining how I would plan such a thing, but for the purposes of fiction, it’s also useful to consider how things could go completely wrong. What if not all the ships made it, and something really important was on a ship that didn’t? What if conditions on the ground were massively different than expected? What if the characters weren’t planning to make a colony at all, but were stranded without supplies?
One planet and a motley group of people can result in endless possibilities.