The biggest issue with basements is moisture. Not necessarily the liquid kind (sounds like you've got that under control) but water vapor that comes in all the time from the soil and through the concrete. Moisture needs to be handled in the right way, and a lot of contractors use plastic-which may meet code, but it is often not the correct way. (Plastic sheeting, especially on the "room side" of the walll, is going to cause a lot of trouble). Likewise, fiberglass insulation on the basement walls is a risky business-it can invite tremendous mold problems. Foam insulation--correctly applied so as to prevent interior air from reaching the cold concrete walls (causing condensation--> mold) is a good bet. It will also allow a limited amount of water vapor to pass through the wall, so the wall dries to the inside. That's good. Expanded Polystyrene (EPS) foam (usually white, often called "beadboard") dries better than Extruded Polystyrene (XPS) foam (the blue or pink stuff). EPS is also cheaper. Glue the stuff up, fasten wood battens through it and into your concrete/block, and attach your drywall to the wood battens. Mold lives on cellulose, and cellulose (paper) is what is on both sides of common drywall. So, if you want to be sure you're not creating a mold habitat, use the drywall that has fiberglass on both faces instead of paper ("densearmor" is one type, I think there are others.) It's not as cheap or widely available as the regular stuff, but if you've ever torn open a basement wall and looked at the back side of the drywall, you'll want to use this type of non-cellulose product.
Carpet on the floor: very comfortable, but often not a good idea in a basement. The concrete floor (under the carpet) will be below the dew point of the air, and there will be condensation that micro-organisms will love. The stuff that accumulates in the carpet padding is a feast for them. When finished basements smell bad, it's often because there's carpet in them. Maybe throw-rugs you can at least remove and thoroughly clean occasionally?
Here's the best site I know on this topic. It's from the folks at Building Science Corporation, and they've done a lot of research into this, have seen what works and what doesn't, and aren't trying to sell a particular product/system.
BSD-103: Understanding Basements —
Sounds like a great project. Good luck.