I live in SW Ohio and made my first trip to SD last year. I went alone with my dog. I stayed in Mitchell and hunted from there. One thing I learned is everything in SD is an hour away. There is plenty of public land, but the drive between can be long. I planned each day out so I had a general route to go.
As far as crowds I went during the week around Nov 10th and only ran into group at on spot. They had about 10 hunters and 6-7 dogs. They got on line and flushed a field. I stayed across the road and found all kinds of birds.
A couple of things I learned from my first trip. If you have a pointer they may struggle with wild birds. Pheasants don't like to hold if they can run. My dog also lost a significant amount of weight, even though she was eating a good food and I doubled up the amount. We hunted all day and it is a lot of running for them. This year I may plan a rest day. The wind in SD is no joke if the local news says it is going to be windy, it will almost knock you down. The game wardens are friendly and helpful. In fact everybody I met out there was very friendly. They will give you advice or help if you need it. Do nt slam your truck doors, in fact stop down the road and get your dog ready and gun out of its case but unloaded. The pheasants will be watching as soon as you pull up. And the will take off as soon as they can. I had the most luck in waterfowl management areas.
People have mentioned it before, but always have fuel, it is a long way between towns. Roads in SD end for no reason, even if they are on a map. Apparently you can put a fence across a road and block it for your cattle. So be prepared to have to back track a bit.
I only hunted public land. I am willing to pay a trespass fee, but I'm not sure how that works. There are fields, but no houses within miles, so I'm not sure how you find the people to pay and I did not ask.
I can't say enough about how great the people and hunting are in SD. I can't wait to go back. I'm still planning on going in earlier nov if your going to be there around then message means maybe we can meet up.