In addition to being a rocketry enthusiast, I have some small experience as a parachutist and as a rigger.
Briefly, I store my rocketry parachutes after doing the following:
1) pulled under tension, swivel to apex, until tight
2) each gore flaked out and smoothed
3) equal number of gores on both sides
4) skirt folded at a 45, both sides
5) canopy s-folded on top of the 45 degree folds
6) slid into a zip lock baggie, lines s-folded to follow
Mostly I do this because it makes packing for the next flight easier.
If you have a particular packing method you like, you may consider just packing it into a deployment bag as you would do for flight. The China Lake study by the Navy showed that parachutes packed for several years opened no slower than those packed for 60 days.
All the best, James