It's better to disassemble the whole thing and keep the shells, hardware, and heads separate. Hassle lang pag buo mo sya stinore, tapos kinalawang yung bolts mo, nastuck sa lugs, nagwarp yung shell sa init, ganun. Besides, you'd end up disassembling the whole thing again to clean and tune up so you might as well store it all separately.
Store in a cool, dry place! I bought my drums second hand and the previous owner stored the kit in some damp storeroom and the bolts inside the rack toms rusted, and random drums got black mould. Put the bolts in little ziplock bags, the heads in their boxes (or any box that fits), cymbals in a bag/case with plastic sleeves or dividers, and the hoops in a box too, maybe. It also helps to have a lot of those silica gel things to keep rust and mould away. Tinatago ko yung mga silica gel na kasama ng toner ng printer sa office to keep all my gear dry hehehehe.