Let's consider a truly outlandish scenario. A device has been invented which can show the future or the past. Experiments show that it is 100% accurate. Someone using this device discovers that in a few years, the earth will be invaded and conquered by aliens and that most of humanity will die off. Around the same time, someone else invents a device that allows one-way time travel to either the future or the past. After some discussion, a group of scientists decide to establish a colony in the late Cretaceous period a few thousand years before the KT impact and extinction event.
Why try to establish a colony under those conditions? There are several practical reasons. First, by choosing an era that has no other people, they avoid competition with any group that is larger and has better knowledge of how to survive in that environment. Second, they can introduce useful livestock to that period and be assured they will become plentiful as such creatures would have no natural predators in that era. Third, the knowledge that a catastrophe is looming will motivate the original settlers and their descendants to focus their efforts on surviving.
Some of the difficulties such a group would encounter include the need for a common language and the fact that any technology they bring with them will eventually stop working. All the modern conveniences we take for granted require a complex global supply chain which is impossible for any group of people to quickly recreate. This would then force them to focus on survival skills as well as creating a culture that encourages population growth.
A good first step would be to introduce some game animals to settlement zone and give them a few years to multiply. Rabbits, turkeys, and wild pigs would probably work. That would give the settlers some easy game to hunt as they adapt to the new environment. To get farming started, the settlers could bring potatoes to grow, as that is probably the easiest staple crop to cultivate. Goats would be another good choice as they are tolerant of many conditions. Hemp fiber can be used for both cloth and rope, so that would be another essential plant to bring.
Supposing once more that time paradoxes are not an issue, another good time and place for colonization would be North America just after the Beringia land bridge vanished. The climate and other general conditions of that time are not substantially different from the present.
The true limiting conditions are: what is the smallest group of people needed to establish a permanent settlement? The first European colonies in North America were reinforced several times and would not have survived without help from the natives. The Pitcairn survivors had a total of 15 men and 11 women. Roughly speaking, it seems that about 30 men and women is the smallest group of people that can be viable long-term. It's interesting to note that a crucial element in the group's survival was a common language and religion. In the first years, most of the men died either by murder or disease.
The best things to take along, I imagine, would be hand tools and camping gear. Eventually, it would become necessary to relearn how to make stone tools until the population grows large enough to support industry. It took the Pitcairn group 66 years for their population to grow by six-fold. Assuming a similar growth rate, a colony that starts with 30 people would grow to about 1,000 after 130 years and it would take another 130 years to reach about 36,000.
In general, infant mortality would be high, though at least modern knowledge would help that somewhat. Books would not be as important at first as tools, but eventually, there would be a need for future generations to be educated so that it would not be necessary to re-invent and re-discover everything. The greatest danger to human life after disease is violence. I have a hard time seeing how a multicultural group of settlers could survive, but perhaps it could be done. There were about 400 people in the first wave of immigrants to Iceland, and they shared a common religion, language, and culture.
Given the nature of linguistic evolution, whatever books are brought to the past would likely be unreadable to future generations after a few centuries. A remedy to that would be to use a logographic writing system like Chinese.
It's fun to think about these questions as time travel migration presents many of the same problems as the colonization of other planets.
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