I started out using cut-down grocery store cardboard boxes, like some here mentioned. The ones they sit on the shelf with canned goods sitting in them are easy to get at the local grocery store, as are many others of varying sizes. I pick up a few every chance I get. The sturdier, the better but beggers can't always be choosers, so I take what I can get. I line them with a bit of paper towel on the bottom, then add some plastic mesh material to lift the soap a bit and add a bit to the air below the soap. These stack easily in alternating directions.
I also have some of those 'legs' that restaurants use to put food trays on when the wait staff bring you your order, and I have some of those large trays they use, too. I set one of those at the foot of the bed and directly under the ceiling fan in a spare room. That's where the most recently cut soaps sit. They are moved to the 'stacks' on the bed (a cardboard layer protects the bedspread) in the same room. I also have a desk in that room with a rubber/plastic coated wire rack (with 3 or 4 shelves) that sits inside a cardboard cut-down box (to collect soap debris) where I also have some soap curing.
When they are cured sufficiently and I start labeling them, I move them to another room (granddaugher's bedroom, actually, but she doesn't visit often, so it's not used much) where I have a similar set-up for stacking wrapped and labeled soaps.
Just yesterday I bought two plastic Coca-Cola trays (black plastic trays made to hold cans of Coke) at the Goodwill for $1.98! They ice thing about them is they nest inside each other and have plenty of air holes built right in. I stacked the soaps I've made on this trip and can easily move them about until I get them home and integrate them into the curing set up I already have in place.
Periodically I make purchases of whatever I think will work, especially if it's in good condition, coated with rubber or plastic and priced as low as seems a bargain to me, especially when I can find them at Thrift Stores. Plastic Mesh used for needlework is good to lift soap up off a completely flat surface, and I just got a package of 16 for only $2 at a WalMart here in San Antonio last week. It was a real find, because they normally cost more. I also use rolls of plastic mesh that is used in restaurants and bars to sit drinking glasses, etc. on top of on shelves. I had a bunch of that stuff left over from when we had the restaurant, but have used it all inside of the cardboard 'trays', therefore continue to purchase more as needed.