How should I insulate basement walls and floor after water mitigation?

I know it's popular, but putting a finish surface on a basement cement wall doesn't seem clever at all. A cement wall is a perfectly presentable wall surface, it is a basement, after all; you'll not fool anyone into forgetting they are in a basement.

The problem with covering it up with an "appealing" wall finish is now you cannot inspect the wall. I get where your idea is that you'll have a leak-catcher system, but if anything goes wrong with that, you'll have a mold nightmare lickety split. And a lot of expense on both sides: installing the wall in the first place, and tearing it out.

If you really want to insulate the wall, install a vapor barrier and insulate outside, digging if necessary. That will place the wall mass inside the insulation envelope so it will help regulate interior temperature; the mass becomes your friend instead of your enemy.

I won't get into the other concerns you have in your basement - I will just understand it could get wet. You are in zone 5 in the US. There is no reason for direct insulation on the lower walls.

I would use something a little bit more mold resistant like mineral wool and only insulate 1 foot past grade. That means you will need to cut crossers to hold the insulation 1 foot below grade. The insulation even if you basement gets wet should never be near water and if it ever is that is the last thing you are worried about.