Storage is the first conservation act. Stable moderate temperature, relative humidity roughly in the 40–55% band, darkness and clean air cover most risks; the enemies are damp (corrosion), dryness extremes (cracked dials and shrunken wood), light (faded dials and lume degradation) and pollutants. A closed drawer in a lived-in room is usually better than a damp basement or a hot attic.
Decide a policy on running. There is honest disagreement here: some argue a watch kept clean, lubricated and run periodically stays healthier than one left dry for decades; others prefer to store significant pieces unwound and untouched. What is not defensible is running a watch whose service state is unknown — old oil turns abrasive, and wear from running dry is permanent.
Document everything, in a form that survives you. For each piece record: what it is, how it was identified, what evidence supports that, where and when it was acquired, what has been done to it, and photographs. Keep the records exportable and backed up — a collection database that dies with its owner's hard drive is a loss to everyone who comes after.
Resist cosmetic improvement. Polished cases, refinished dials and replaced hands may please the eye today, but they erase evidence and, increasingly, value. The market and the museums have both moved toward originality; the safest long-term strategy is to preserve what is there.
Finally, plan the handover. A collection with clear records, honest descriptions and named significance can go to the right next home — family, museum or market. An undocumented accumulation becomes a problem for someone else to solve, and the knowledge assembled over a lifetime is the part most easily lost.