Man, you guys are being WAY too optimistic. If we’re starting with 3000 people, you’re not going to see an advanced civilization again for generations, if for no other reason that sheer lack of manpower. Think about how many people it takes to make something as complex as an engine - How many miners, how many people to transport ore, to smelt it, to build sand castings, pourings, extrusions… Then there’s the rubber for insulation for wiring and tires and seals and such, which requires harvesting the rubber itself, vulcanizing it, etc. Then there’s the petroleum, construction of cracking plants, the list goes on.
And remember, this is only one very small piece of technology. And you still people to grow food, built shelters, teach children, etc. ad infinitum.
Even assuming that our colonists walked into a WHOLE WORLD fully stocked with today’s technology, it would take generations before they had enough people to operate everything, by which time most of it would be in ruins.
I think that the minumum population you need to sustain a technological society is on the order of millions of people. Hell, you probably need several thousand people just to maintain production of ball bearings.
Then think of all the specialized trades you need to maintain even a middle-tech society: Saddlemakers, blacksmiths, tool and die pros, miners, seamstresses, loom makers, carpenters, (nail makers!), the list goes on.
My personal opinion is that allowing the colony to bring along a few thousand pounds of goods will give them a more comfortable life, and greatly increase the chance of the colony surviving and thriving, but it won’t do much to shorten the time it takes to get back to a 20th century technological level.
All the tools and equipment they bring are going to wear out, and they won’t be able to replace all but a small fraction of them. So they need to prepare for the 18th century lifestyle their children’s children are going to have to lead.
The first thing I’d bring is a nuclear reactor. Something like the nuclear electric generator on the Cassini mission, only at a slightly larger scale. Double or triple the spares for anything that could wear out or degrade. This thing would form the core of the colony - with enough power, you can achieve anything, and a nuclear generator could last for hundreds of years. That means heat, light, power for tools, electric fences to keep out predators, etc.
Then lots of basic tools. Not fancy, just very high quality. Wheelbarrow hardware (you can carve the wood frame for it later), saws, axe heads (make axe handles later), titanium drill bits and saw blades by the gross, etc.
Forget cows if we’re limited by weight or volume. They’re inefficient. Bring a few male goats, dogs, sheep, and other small useful animals, plus lots of young, pregnant females. The cheapest way to take your animals is as embryos inside mom. One male can fertilize lots of females, so you want to take like a 10-1 ratio of females to males.
There are a few small machines that could last a long, long time and be incredibly useful. Treadle operated Singer sewing machines, metal looms, spinning wheels. Load up on those.
Forget anything high tech. Computers only last a few years, and will never be replaced. Gas engines need gas and wear out fast.