It seems you have made the decision to update the space. I totally understand your desire to do the update over time on your schedule. DIY'ing everything?

Here would be my probable event sequence.

Sounds like your basement was dug before a requirement for egress windows so a grandfather clause should prevent your having to install one provided, as you say, this isn't living space.

Develop a scale drawing for everything in the finished space. Include walls, lights/outlets/switches and any features to build around (stairs / mechanicals) or added (Powder Room/Bar etc.) Place masking tape on the floor for wall location(s), can lights and anything else planned. This will force you to completely think through the build, develop a materials list and enable you to begin shopping even before beginning the project. I'd include a back-up sump pump as further protection for the investment.

Remove the carpet.

Remove the existing drywall and insulation. Now you can inspect the existing studs and the construction quality. Possibly you can leave many in place. Kill any mold and replace any infected studs.

Now is when you need to think about permitting. Know the requirements! Talk with them, submit the plan for review and approval. You'll probably need plumbing/electrical/insulation and final inspections.

HVAC? If you have forced air at minimum install a cold air return. Generally minimal heat will be necessary for a basement except seasonally (spring/fall) when auxiliary may be necessary. I installed an electric fireplace to accomplish this.

Any plumbing required? You don't mention the need.

Proceed with electrical. Inspection upon completion.

Have expansive foam insulation installed professionally, then have the insulation inspection.

Drywall. Not familiar with Thermex so can't advise.

Final inspection.

Recarpet or tile the floors. Trim the doors/walls.

I'm sure this is a simplistic overview absent more specific facts. Good luck.

Since budget seems to be a big concern, you might want to avoid Dupont Thermax, a high-end commercial product.

Ditto closed cell spray foam, which will likely cost at least four times more than diy installed XPS (extruded polystyrene) or EPS (expanded polystyrene).

I've successfully installed low pile commercial carpet directly glued to new basement floors. I would be dubious though on using it on an old floor, but would instead suggest Delta FL followed by plywood. Or, keeping that budget in mind, simply concrete floor paint and area rugs that can be regularly lifted and cleaned. Nothing rubber backed!

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Whether its' grandfathered in or not, I would add an egress window or door to any basements I planned to use. The consequences in case of fire are too grim (and common) to contemplate.

Here is a link that might be useful: Building Science Corp. on basements

Thanks, fnmroberts and worthy. I appreciate your comments. Definitely things to ponder as we explore options.

While there is currently a W/D hookup and some outlets, the plan is to leave all that stuff as is. I don't want to add/remove any walls, replace windows, etc. We just really need to get rid of that carpet, and I'd rather replace the batting insulation with something suitable as my understanding is it can cause problems below grade. No sense in patching my 4 foot gap if I should be replacing it all.

Plus given what we've seen in this house, I'm not sure I should trust the walls down there to be built right. Given what we've already put into this house and how little time we are/would actually spend down there, it's a project I'd DIY as much as I could. I wouldn't cut corners with things, but wouldn't go top of the line either.

I'm almost crazy enough to try a DIY egress window, but not quite! I'd definitely plan for one so it's easier down the road, but unless we end up spending some time down there it might get put off indefinitely. It's a finished area, but not to the point of being a functional additional floor. Ceilings are on the low side, heating is not great, and it's a bit dark. Fine for laundry or a few rounds of pinball, but not a place to really hang out.