Moisture is genuinely the killer here, and you can't skip that step. Before you touch any insulation, get down there and spend a few days watching the concrete. Does water actually pool or seep up, or is it just cold and slightly damp to the touch? That changes everything. A simple test: lay down a plastic sheet for 48 hours and see if condensation forms underneath or if water beads up on top of the concrete. This tells you whether you're dealing with rising damp or just surface moisture from temperature differences.
Once you know what you're facing, the moisture barrier comes first - that's non-negotiable. A good quality damp-proof membrane (roll it out before anything else) stops capillary rise from the ground. After that, rigid foam boards like XPS work better than soft underlay for old properties because they won't compress over time and they handle any residual moisture better. You can lay them straight on top of the membrane, then add a floating wooden floor or self-leveling compound over the boards. The key is leaving a small air gap around the edges so moisture can still breathe out at the perimeter - seal it too tight and you're just moving the problem around.
I've seen folks try the cork route thinking it's magical, and sometimes it helps, but honestly it's not fixing the fundamental issue if moisture's your real problem. Stick with the order: test first, install membrane, then rigid insulation, then your floor surface. Skip any step and you'll be tearing it up in a few years. It's tedious upfront but it actually works for older buildings.