My process is time intensive, so it wouldn't do for most commercial work, but I like the results for one-off woodworking projects.
First, I sand to 600 grit dry. Occasionally I sand to 1000 or 1500 dry. Sometimes I leave it at that, sometimes I wet sand as I'm applying oil. I'll go up to between 1000 and 2000 when wet sanding.
I'm a big fan of sanding to high grits because it brings out the fine detail in the wood. However, for that to be meaningful, you have to be working on a scale where people will see the fine detail. Nice custom furniture pieces meet the criteria for me, kitchen cabinets do not, unless you are doing something out of the ordinary with the wood. I don't use stain if I can avoid it, as I normally choose wood carefully and don't want stain to get in the way. My goal is to take advantage of the natural features of the grain, and I think stain obscures those features.
I use mixes of polyurethane, linseed oil, and orange oil (as a mineral spirits replacement - smells a lot better). First coats are high on orange oil (40%) and linseed oil (40%). Later coats are high on polyurethane (50%). For things that don't have to be water resistant, I generally do 4-6 coats of oil and 2 coats of BriWax. If I want to be super compulsive, I may do a couple of extra coats to wet sand to 2000 grit. Overall, my goal is to get a finish that is part of the wood, rather than sitting on top.
One of the big advantages of this kind of finish is that is is easily renewable. I have several very nice pieces of furniture that I have re-oiled and waxed (one a couple of times) due to grandchild wear and tear. I even was able to take some water marks off. They still look fantastic.
Note that I wouldn't recommend this for architectural woodwork or kitchen cabinets. Besides the fact that it's too time intensive, I don't think that the oil finish would hold up to a kitchen environment. I did some custom book matched #3 cherry panels for a set of kitchen cabinet doors that I did sand to 800 grit, but I ended up putting a hard finish on them.
I've never tried Osmo, but I'd like to at some point. I'm also intrigued by catalyzed oil finishes like Rubio, but I'd want to experiment with that and it's pretty expensive stuff to experiment with.
And... if Festo ever expands their robotic lines to include a sanding/finishing robot, and I win the lottery, I'll be all in

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