If the Minwax stain is used, no sanding sealer is neccessary as the stain sets the grain. It you want unstained wood, a sanding sealer is recommended.

At Home Depot, Varathane Floor Oil finish is the more premium and more expensive. It contains microscopic aluminum oxide particles to increase wear. That is the stuff sandpaper is made from. It requires a minimum of two coats over a stain, but 3coats is highly advisable to increase the long term wear. As mentioned, it does have a slight amber tone to it and will get more so with age. This is important if a light, whiteish stain is used. Better then to use the water based.

Water soluble urethanes are increasingly popular because they dry quickly and multiple coats can be put on in a day. They also have relatively little odor. A minimum of 4 coats is generally recommended with these because the film is thinner. Many feel that the water borne products lack the warmth of the oil based due to their crystal clear color. This can be partially alleviated by using a de-waxed, or "universal sealer" as the first coat. DO NOT use regular shellac, as it is not compatible with urethanes. Shellac gives a nice warm patina which helps the water bourne urethane avoid that plastic look. Shellac is also very fast drying.

Allication of floor finishes is normally by use of a floor applicator on a b room stick; lambs wood for oil, synthetic for water based. A brush is used to cut in the edges. I have seen the pros just pour the varnish on the floor and kind of squeegee it
along the floor in a kind of figure eight pattern.

You definitely want to follow the directions on the can. Urethanes are kind of funny in that they have a window in which additional coats can be applied without sanding, usually between 4 to 12 hours. Once thouroughly dried, it has to be "screened" or sanded before additional coats. So, try to stay in that 4 to 12 hour window to avoid repeated sandings. Of course, if you have managed to get crude into the varnish, it can always be sanded and dusted before continuing.

As to how environmentally friendly shellac is: it is grain alcohol (de-natured) with shellac flakes desolved in it. What is more organic than beatle droppings! It is harmless enough that medication pills are coated with it! It is about as time tested as a product can be. The Chinese have been using it for a couple thousand years! I guess they didn't know that there is no lead or melamine in it!