The single most important thing is fixing the moisture source first - whether that's grading, gutters, or drainage issues - because even the best membrane will fail if water keeps hammering the foundation from outside. I've seen plenty of basements where folks slapped on a membrane and called it good, only to have problems come back because water was still pooling against the foundation.
For actual products, you've got solid options in both categories. Liquid-applied membranes like Tremco's Vulkem or Carlisle's water-based coatings are pretty forgiving to work with and handle small cracks well since they self-level. Sheet membranes like Grace Ice & Water Shield or similar rubberized products give you more reliable coverage if you get the seams right, though installation is more technique-dependent. Most contractors I know lean liquid for DIY basement work since the learning curve is lower - you basically brush or spray it on, and it cures to a rubbery finish. Sheet membranes need careful overlaps and good adhesion, which is where people mess up.
What I'd do for a 70s basement is go with a two-part approach: apply a liquid membrane (something like Drylok or similar if you're handling it yourself), then add a dimpled drainage board over top if you have the wall clearance. The dimples create an air gap and give water a path down to your perimeter drain or sump. Make sure your foundation is clean and dry before you start, patch any active cracks with hydraulic cement, and give yourself proper ventilation while it cures. If you're getting significant seepage rather than just dampness, honestly consider whether you need interior or exterior French drains - the membrane buys you time but won't stop active water intrusion.