What kind of group would you send back, and how would you prepare them? The OP said several thousand, and 3000 came up later, so let’s say we have a way of sending 3000 people to this alternate universe/prehistoric time.
First things first, if this is a serious project with strong governmental support (as most colonization attempts would be) the people sent will be the absolute best for whatever role they are to accept, and this is going to be planned out extensively ahead of time. Here’s how I’d do it. A chain of command and a way of enforcing pre-agreed upon rules will be organized.
A good percentage of those sent back will have been trained in use of primitive weaponry and appropriate tactics (probably ex-military folks), psychological profiling will make sure that all these people are the kind who are cool-headed yet unswervingly loyal. They will also be cross-trained in other outdoorsman-type skills that they may not already have been trained in - they will be the primary hunters and explorers in times of peace to keep them busy. I’m not sure what percentage of the population this group will have to make up - their primary purpose, of course, is to enforce the law and keep people from straying from the plan but I’m not sure what kind of numbers advantage they would need in case of a ‘civillian’ revolt with the weapons they will have - bows, crossbows, and polearms almost immediately, and they shouldn’t have to upgrade for a while as long as they keep the rest of the population disarmed. I’m pretty sure that 20% (600) could keep the other 80% under control if the 80% is limited to common tools as weapons and they are not allowed to train for combat or assemble in large groups. It should be easy for them to maintain control, they are going to be providing a great deal of the food at the beginning and later will have free time to keep a close eye on everybody else.
The majority of the population is going to have to work, and hard. No time is to be wasted, and there will always be a next stage of colony development that can be worked on and if there is no farming to be done you will be working on something else. If everything necessary is already complete, you will be put to work building infrastructure for later generations, i.e. clearing new fields when there is already more than enough food production, building furnaces before the ore is mined. There will be experts in many different fields, many of which will not be immediately useful, but since we are choosing from a large population whenever possible they will be physically fit people who can provide muscle power when it is needed, all will be trained to have basic knowledge of subjects like farming, basic engineering, brickmaking, etc. and everybody will have at least a couple of skills they are very good at, chosen for what is needed with some to spare - if the bean counters decide that the building projects planned for the first 20 years require at least 100 highly-skilled carpenters to supervise, they will make sure at least 300 of the people are skilled carpenters. Bring several experts in each of the fields of knowledge that are expected to be important later in the colonies development - at least one at any time will spend most of their waking hours recording their knowledge (perhaps in clay tablets) and teaching those of the younger generation when they arrive.
Not everyone is to be highly educated, though everybody will be expected to have some useful or potentially useful skills - I think a colony of 3000 college graduates, no matter how carefully they are screened, is the safest bet for a stable and highly rigid society. A good deal, maybe most, should be people of decidedly average intellect and ambition. If they wonder why they were chosen to come along with all these super-achievers and geniuses, tell them it was to provide genetic diversity. It won’t exactly be a lie.
We are going to want to bring as much information as we can. If this scenario permits us bringing books then some of the options below can be discarded, though I don’t think that really fits in with the concept of starting with nothing, so I’m going to assume we can’t bring anything but our bodies (kinda like the time travel in Terminator). In this case several of the people chosen to go back will be picked because they have eidetic memory or other similar exceptional memory traits (like those people who can recite entire volumes from memory) and they will be taught (or chosen because they know) important information. If there is other data that cannot be readily memorized accurately it will be compressed and tattooed in code and/or diagrams on the bodies of some (or all?) of the colonists. Upon arrival the process of transcribing this information from minds and skin to more durable media will begin immediately. If someone dies before their tattoos are copied their skin will be preserved until it can be copied.
The government will have one primary leader, with council of a dozen or two below him, each assigned to governing a certain project or aspect of life. There will be a constitution of sorts that has strict guidelines on what should be done under most foreseeable circumstances. Decisions on problems that were not foreseen must be agreed upon by 3/4 of the council, if 3/4 can’t agree the decision is made by the leader. The leader position will cycle through the various council members in a predetermined order, with a fairly short term (1 year perhaps). Public meetings will be held regularly, and a 3/4 vote can remove any council member from office, who will be replaced by the next one on the list of succession, which will include the entire original population, so even if 9/10 of the population is wiped out there will be no question who should be leading. The council must reach a unanimous decision to remove the leader, unless he clearly is trying to lead the colony in a way that is contradictory to the constitution and guidlelines.
All the laws will be pragmatic, written around the primary objective of maintaining the colonies existence and progress. Laws will prohibit damaging infrastructure, wasting food or resources, refusing to perform your assigned duties, refusing to contribute to the breeding program, and endangering yourself and others. Things will be hard enough on the people that we will not need laws prohibiting things that will not adversely effect the colony in one of the ways listed above. A wide variety of punishments will be used - removing privileges, corporal punishment, imprisonment, slavery. There will be no true death ‘penalty’, but those who have progressed all the way through the list of punishments to slavery and still refuse to contribute to the colony will be put to death as everybody has to (at least) carry their own weight and the colony cannot afford to have that drain on it’s resources. Those who show a pattern of causing serious damage to the colony and are therefore a threat will also be put to death - examples would be someone who murders or maims repeatedly, or who repeatedly and willfully damages important colony assets. We really want to minimize reducing our population more than necessary, though.
With this plan, I can see a fairly advanced and diverse society in a couple of hundred years, probably at an early industrial level with steam engines, firearms, and a fairly high standard of living for most people. By this time there will be a steady flow of people leaving the first settlement to work in new ones (probably at first exploiting important resources unavailable at the first site) or to set up self-sufficient homesteads in the wilderness. They will be able to expand much faster than they will - we don’t want them too scattered, most the population should remain in the original city. Once the first city is thoroughly established, perhaps other cities will be allowed to adopt their own independent governments though the advantages of being affiliated with the first and most powerful might make it unlikely for a while.