As the title states, I have a Michigan Style Basement.

The floor and half walls are concrete, though the 'shelf floor' that is approximately 2-3 feet from the outter footings is dirt.

What I would like to do is insulate  to reduce moisture in the summer. I need to run a de-humidifier from the start of the spring to fall to pull the moisture out of the air.

What would be the best way to approach this?

Some options I am considering are:

dig a few inches of dirt out of the shelf floor and fill it with mixed concrete. From there I could use rigid foam to cover the walls and shelf floor (now concrete) and tape the seams?
or,

Build a 2x4 floor out of treated lumber to cover the dirt floor, then rigid insullation to cover it as well as the concrete walls?

I am not trying to turn the basement in to livable space, it contains my washer/dryer/water heater/furnace.

I would like to eventually put a small electric sauna down there w/proper ventilation for the steam.

But even if that is not an option, I still want to reduce moisture and up the R-value.

Thanks in advance.

1. dig 4" of dirt out of the shelf floor, install 2" of EPS or XPS, taping the seams. Install 6 mil poly and tape those seams. The poly should extend up onto the wall.
then pour a 2" concrete floor. Note that the foam must extend up the wall enough to disconnect the new floor from any other floor or wall concrete.

2. Install Polysio aluminum faced foam - 2" minimum - on the concrete walls with foam adhesive (this must have a fire barrier over it unless you use Thermax brand) Foam the seams, the top edge and the bottom edge, then tape them.

3. Glue 2" of XPS or EPS foam on top of your cellar floor, tape the seams. Pour 2" of concrete over this if possible, installing a layer of 6 mil poly (taped) between the foam and the concrete. If pouring a new 2" floor over the existing floor is impossible, you can cover the foam with exterior grade plywood. If you can install the 2" of concrete in the main basement, put strips of 2" foam around the edges so the new concrete does not touch the cold concrete. This prevents a "thermal bridge" which will draw heat out of the concrete.

Moisture comes up from the ground below the house, and through the walls, through the concrete, so you must prevent that moisture from entering the basement. Adding a layer of foam does two things: it isolates the basement from the cold concrete, lowering condensation levels, and when installed under concrete which is isolated from the walls, allows the new concrete to remain at or closer to room temperature. Polysio aluminum faced foam is an excellent moisture barrier on walls, but should not be used under floors where it can absorb water. XPS (Styrofoam) is permeable, but less so than EPS, will help keep ground moisture out of the basement, and can be used in potentially wet areas.

I had a very damp - occasionally wet - dirt floor basement; I installed 2" foam, 10mil poly and concrete. the basement now is usable for storage and workshop, with a stable, comfortable heat level. And it increased the comfort of the whole house by a huge amount.

I like your method.

A couple of questions.

Is there an alternative to concrete that will work just as well? Could I use treated lumber? Or, filling it with gravel an option?
 

If not,

What would be the best way to mix concrete? I would be buying bags and mixing it myself and I'd like to do this over the winter so it is done before the moisture sets in.

Can it be mixed outside on warm winter days? How long do I have to pour it? Can it be done in sections? Thanks.

I like your method.

A couple of questions.

Is there an alternative to concrete that will work just as well? Could I use treated lumber? Or, filling is it with gravel an option?
 

If not,

What would be the best way to mix concrete? I would be buying bags and mixing it myself and I'd like to do this over the winter so it is done before the moisture sets in.

Can it be mixed outside on warm winter days? How long do I have to pour it? Can it be done in sections? Thanks.

IMHO you're not going to successfully pour a floor like that by mixing bags from the hardware store. You're going to need a concrete truck or two, and some friends. If you are lucky you will be able to fit a chute through a couple basement windows so you won't have to wheelbarrow all of it.
You could also have it pumped in.