furring is NOT structural its a solid shim. use what ever you want. I think you are over thinking this whole project. Here’s what I would do:
scrap off anything loose including molds. drylock over any barespots. use pressure treated lumber on bottom plates. frame up walls as you normally would, leave a 1" gap between concrete and wood. insulate with craft faced insulation and drywall. use the vapor barrier if you must. There are as many good reasons to as not to. Definately put a dehumdifier in basement. Always keep it running. you can run drain into sump pit. If dehumidifier is running, everything will remain dry. the vapor barrier would actually HURT by blocking the moisure where the dehidifier will not dry out behind it. (I would not use one)