I agree with Steven about Dricore. I have used it and it is terrific for
- creating a moisture barrier
- giving a slightly softer feel underfoot than concrete
- serving as a great subfloor for almost any type of surface
However, I would seal the floor first (which I did) with a wateproofing product like Drylok.
One caution - do not seal the floor under a water pressure tank or filter system that sweats in the summer. Condensation from these systems often drip down and dissipate through raw concrete, but will pool if you seal it.
Keep the dehumidifier going. The moisture is still in the soil surrounding the foundation and will probably still percolate through the walls.
I remember Neillsville from "The Rock" radio station. ;)
So, to answer the question, we need to know where the water is coming from. You mention that it's due to a high water table.
As such, I'd not ever finish the basement. It will always be one power outage or one clogged drain away from being ruined again.
It also means that your dehumidifier will never 'win'. Basements are moist by default simply due to cooler temps, but if you have constant hydrostatic pressure, it will always be an uphill battle.
Your (what I call) interior footer drain will certainly help, but you're at the mercy of the drains always remaining unclogged and the sump pump always having power. You'll also have to make sure it can handle excessive rain during those big midwestern downpours.
If it was merely an occasional rain/snow melt issue, I'd feel OK finishing the basement, but given the high water table, I'd consider rethinking doing a full finish project down there.
If your water problems are primarily at the footer, It may be OK. As that is exactly what the drain system is designed to handle. But if you have actual cracks in the walls and water is coming in there, I'd be definitely be hesitant.
One other note...a bit further west into MN, the clay soil we were on had a lot of radon. So you may want to get a radon test before thinking of finishing the space as well.
Oh, one last comment: note that the systems being proposed are in no way 'waterproofing' systems. They are water abatement systems--in that they are designed specifically to not be waterproof and actually allow the water to come in so it can be moved out. It's a nit-pick, for sure, but actual waterproofing is an entirely different discussion.
Best Answer
Taking air out of the house like that would mean getting more fresh air into the house. A little would be good. A lot could result in drafts in strange places as the air would come in from wherever it can. The effect would likely be uneven as some areas, perhaps with leaky doors/windows, would get a lot of fresh air and others would get almost none.
In addition, the air coming in would be as hot/cold and humid as the outside. That would help feel less musty but not necessarily less damp or feel "good".
A quick search finds that central vacuum typically uses 2" ductwork where HVAC typically 6" or larger. That being said, perhaps an inventive HVAC tech. could come up with a solution to use the central vacuum ductwork for an HVAC system. Or possibly a mixture - use traditional HVAC ductwork for the easiest runs (and/or the rooms that need it the most, like the kitchen) and use the central vacuum ductwork for the rest.