Rigid foam boards are usually your best bet for a damp basement because they resist moisture way better than fiberglass batts, and they also give you better vapor barrier protection. For a typical basement, you're looking at somewhere in the $1.50 to $3 per square foot for materials - rigid XPS or polyiso foam - depending on the thickness (2 to 3 inches is standard) and whether you go with name brands or contractor-grade stuff. Labor runs maybe $2 to $5 per square foot if you hire someone, but that varies wildly by region and whether they're also doing framing and drywall on top of insulation.
For a semi-detached 1980s house with damp winters, I'd honestly focus on the moisture problem first before you insulate. Get that basement checked for water intrusion or condensation issues - sometimes it's not even that bad once you improve ventilation and drainage outside, or run a dehumidifier. If you skip that step and just slap insulation over a wet wall, you're trapping moisture and asking for mold later.
Total project for an average basement (say 800 to 1,000 square feet of wall space) probably lands you somewhere between $2,500 and $8,000 depending on how much you DIY, the foam type, and whether you're also finishing the whole thing with framing and drywall. Get a few quotes from local contractors who specialize in basements - they'll spot moisture issues you might miss and can recommend whether you need interior or exterior drainage solutions too.