Believe me. I have been down this road before, but never with Wisconsin snow.
"Is it better to start with a little water in the pot to begin with?"
"Should I compact the snow before I add it?"
"Is the older, more compacted snow below the surface better?"
First, you get your stove all ready to go. Then grab your largest melt pot. I usually use an aluminum pot that is about two quarts, although I have used larger and smaller ones. Wander off from camp a bit and find a clean patch of snow. Using the metal lid, you scrape off the top inch of snow, especially since often there are leaves, pine needles, or dirt in it. That top snow is discarded. Then using the main pot, you scoop it full of clean snow, and you can use the metal lid as a scooping tool if necessary. It depends on the consistency of the snow. Return to the stove and light it. While the stove is reaching its normal temperature, you wipe off the bottom of the melt pot with a glove. You don't want ice or snow hanging on the bottom, because that might extinguish the flame. Put the melt pot on the stove, and immediately pour some liquid water through the snow into the pot. If the pot is level, it should not require too much water to completely cover the bottom. A fraction of an inch of water is sufficient. The advantage of pouring the water through the snow in the pot is that it slightly melts the snow and causes it to form better to the hot pot surface. Once that is started, you can put the metal lid on the pot. From then on, it is all about minimizing lost heat, so keep your windscreen there and maybe even put a piece of aluminum foil loosely over the top of the whole thing. This is also one situation when you need the heat reflector underneath the stove burner to keep reflected heat from melting out the surface underneath the burner. While that first pot of snow is melting, return to your snow gathering site with a plastic bag and a shovel. If you don't have a shovel, then you are going to have to steal the metal lid off the snow melt pot.
For an individual, it doesn't take much more than a gallon-size bag. For a group, I have used a large garbage bag. Shovel more clean snow into the bag, and carry it back to the stove. Keep it at arm's reach so that you don't have to keep running out to get more snow for the melt pot. If you do this right, you can do the melting in the vestibule of a tent and keep the snow bag between the tent layers.
Beginner snow campers will soon learn that liquid water is a valuable resource, and you can produce it easily from snow, assuming that you have the right stove and plenty of fuel. Incidentally, this is one area where wood fires are very good. Wood fires are very hot (which you will know if you have ever seen deformed aluminum cookwear). So, if I think that I will be using a wood fire, I take a titanium pot instead.
Very old snow is dense, so about two quarts of snow will yield one quart of water. Very new powder snow is fluffy, so about ten quarts of snow will yield one quart of water. All snow is different.