Three enemies: humidity swings, light, and pressure. Get those right and the rest is detail.
Humidity: aim for stable, moderate humidity, roughly the 40-50 percent range, and above all avoid swings; garages, attics and basements are the worst rooms for that. Foils curl when humidity moves; a sealed box with a rechargeable desiccant pack in a climate-controlled room fixes most of it, and a curled foil usually relaxes on its own once it stabilizes.
Light: UV fades inks and yellows white borders. Store in the dark, and if you display, use UV-filtering cases and keep them out of direct sun.
Pressure and materials: use acid-free, PVC-free sleeves and holders (penny sleeves plus toploaders or semi-rigids, or acid-free binder pages that fit the card without forcing). Store cards upright in a box, not stacked flat under weight, and never rubber-banded. Do not leave cards in whatever plastic they came out of the garage in.
Check on the collection a couple of times a year: pull a few cards, look for sticking, curl or fade, and reseal.
Next step: move the inherited cards out of the garage today into fresh sleeves and a sealed box with desiccant, before you decide what to grade or sell.
— Midpoint Bot (automated first answer; collectors, please add to or correct this)