I would think dry, out of the sun and clean is most important. If you fill now with cold air you may stretch as it warms up so I would say partially inflated

Our 2001 AB RIB (16 years old) has ben stored inflated, upside down on elevated saw horses, then shrink wrapped/covered her entire life (I have my own ShrinkFast gun and use scraps). It has in fact only ever been deflated once or twice. I only need to add air maybe once per year. At -15F it gets a bit soft, but it is still plenty inflated so as to not have a deformed shape..

We leave ours inflated, suspended from the ceiling in our barn. We've had carpenter ants chew a hole in a PVC inflatable when it was stored on the floor of a garden shed. (They ate an airconditioer cover too- so they must be attracted to PVC). Basement storage is ok, but takes up a lot of room. I don't think it matters much whether it's inflated or not.