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.

Thanks so much for responding- I'm trying to line up a contractor get an estimate, but I hate to even begin the process if we've budgeted too little. I don't want to waste their time if we need to wait until Spring to do the project. The egress is priority #1 and will be done by a different contractor than the interior work which can wait a few months if necessary. I'm thinking 2-3K for the egress window using one of the Scapewell type products. As far as costs, we're in a suburb of a medium sized city in the South.

AFAIK, egress windows are required for sleeping rooms. Not for rec rooms, etc. Call your city inspections department - they will tell you.

Cutting holes in masonry walls seems to be a very high priced business. I got an estimate for cutting a hole in the brick wall of my garage to add a side door, and the estimate was about $8k, which included the lintel, but did not include actually installing a door. Cutting out for the egress window usually involves digging a large trench in front of the wall, and installing a concrete well that is sealed to the wall. I assume they can buy precast wells, but it is still a large structure that may be expensive to purchase and hard to move into place. I know there are specs for how deep and wide it needs to be to meet code. They also need to use a concrete saw to the cut the wall, which is probably at least 8 inches thick. It is very physical labor, and making cuts in concrete walls is not easy because you have to hold a very heavy saw vertically or horizontally while cutting, and you don't want it to get away from you and cut the wrong thing (like yourself). Bruce