It is apparent very quickly that I did not read the thread title very well, not the posts to it after I was asked to post here. I hope this is taken as I intended. The things I would want on a homestead, not necessarily things in the house.
I no longer live on a homestead (though possibly again in the future), but I will try to answer the question based on when I did and how I would like to live on one again.
A quality walk behind rotary tiller. Just about any good tiller would work for most of what I am inclined to do with them. BCS brand is probably my favorite. If possible I would also like to have a medium size rear tine tiller. Craftsman, Troy-Bilt, or DR Power.
If only one, though, a medium/large BCS with attachments. The tiller can do all kinds of things besides just tilling a garden. One of the reasons I want one is for digging trenches, pits, and other types of earth work. If the ground is worked it is far easier to shovel into a transport of some type.
A large polymer panel greenhouse with keyhole raised beds using a vertical grow aquaponics system with fish tanks installed with just the upper portion above ground. Worm beds to help feed the fish and rabbit hutches to feed the worms.
I would want a comprehensive outdoor harvest kitchen that can be enclosed in inclement weather to process the harvest of plants and animals. Freeze dryers, dehydrators, pressure canners, vacuum sealers, and independent-environmental-condition insulated root cellars.
To provide heat for the various buildings and structures, including a home and set of barns and storage buildings, I would want one or more multi-fuel outside furnaces with solar blowers, pumps, and automatic fuel feed systems. Firewood, coal, waste oil, propane, natural gas, pellets, corn, weed bundles, and just about any other liquid, solid, or gaseous fuel. Each would have a forced air heat output, hydronic hot water heat output for de-icing sidewalks, roofs, driveways, and so on. Any that would be used for residential or food processing would have domestic hot water heating as well.
A multimode power house incorporating vertical axis wind turbines, low-to-the-ground specialty horizontal wind turbines, spiral drop pit micro hydro, PV solar panels, hot air solar panels, hot water solar panels, minimum of three high capacity battery banks. The building would be built as a Faraday cage with most of the other components protected from EMP and HEMP using grounded metal conduit and protection devices on all entry/exit power points.
With those systems I could have an excellent start on a homestead. The orchards, vineyards, pastures, barns, woodlands, ponds, perennial beds, and the rest would be added.
If initial money was available one or more each of a Bobcat skid steer/all-wheel-steer machine with many attachments and a Unimog U500 multipurpose truck with full options and a complete set of applicable attachments. These can be used for gardening in the case of the Bobcat and farming in the case of the Unimog, given the right attachments in each case.
They would be the start of a full-fledged farm, ranch, homestead, and family estate.
I could add so many more things, but I know this is supposed to be just the primary items.
Just my opinion.