Hi, I'm an occasional lurker and quilter.
IMHO - You should definitely NOT store quilts (or any textiles for that matter) in airtight plastic containers for any prolonged period - unless you can guarantee that the air is moisture free and will not promote mould. In a normal home environment that is not possible. I know all those neat plastic tubs are tempting but they can send textiles musty, then mouldy, then rotten. Just put a quilt in one and put it in the back seat of a car on a warm (not hot) day for about 30 minutes and check out the amount of condensation on the box.
Optimum for storing quilts is actually rolled or flat to avoid wear on fold lines. If you have an old large tube roll the quilt around it protected by some acid free tissue paper. Then wrap the roll in a sheet or similar. If you are lucky enough to have a very dry house under the bed is a good place to store the rolls, or on top of freestanding wardrobes. If this is not possible you can buy archive boxes and acid free tissue paper. In fact I seem to remember the Smithsonian used to sell them years ago.
All quilts should be aired flat regularly, and if boxed they should be refolded on different lines to avoid uneven wear.
If all this seems too much smaller quilts will store well in a pillow case in a normal blanket/sheet storage environment, but if you want them to look good they will still need to be aired and refolded regularly - say 3-4 times a year. For larger quilts you can make a bigger drawstring bag for storage. Try to minimise the number of folds though.
One of the best ways to keep a quilt is actually on a bed. If you have a spare room put the quilt on the bed where it can be seen. Just avoid direct UV light.
It all comes down to how much you want to preserve the quilt. These steps are only needed for "precious" quilts that are to be preserved for centuries or more without museum conditions. If you want to pass a quilt on to the next generation then normal use will produce some fading but with sensible care the quilt will outlast the maker.
My best advics would be - ring your local Quilt Guild or Group and ask then for some guidelines or a book reference.