Quantum Stockpiles are spectacularly useful and pretty simple to set up, it's just that the minecart interface is kinda weird and intimidating. Thankfully you don't really need to understand minecarts to use them for stockpiling, since in most QSPs the cart is stationary and you don't even need track.
Set up two stockpiles and a cart stop as so:
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Make sure you set the stop to dump on arrival, in this case north. Don't bother to carve track first. Customize the 2x3 lower stockpile. The settings on this stockpile are where you get your selectivity. For the upper stockpile, I just make sure it accepts what I want and set it to take from links only, rather than disallowing anything I don't want, just to save time (i.e. for a magnetite QSP, 2x3 takes nothing but magnetite, taking from anywhere, 1x1 is generic stone pile, taking from links only).
Now make a route. Go to Hauling (h) create a route (r), name it if you like (n), position the cursor on your cart stop, and make a new stop (s). Connect it to your 2x3 feeder pile by moving the cursor to the pile and pressing "s". Press enter, make sure it will take what you want. Don't worry about making it too specific, since it can't take anything that isn't in your feeder pile. Press escape to go back to routes, use "v"to assign a cart to the route.
You now have a working quantum stockpile! Dwarves will load stuff from the 2x3 feeder pile (there's no reason it has to be 2x3) into the cart. Since the cart is sitting on a dumping track stop, the stuff will be immediately dumped onto the 1x1 tile (assuming you remembered to make the stop dump, and in the right direction. It's very easy to forget). They won't move it off the 1x1 tile, since it is in a valid stockpile tile, despite that tile also containing a few thousand other items.
This does not work with stuff in bins or barrels (though I think it works with bins and barrels themselves in furniture piles) because the 1x1 pile can have the allowed bin or barrel number set no higher than 1, and dwarves will take the excess containers and put them back in the feeder pile, even if you set up stockpile links such that they shouldn't. I haven't found a workaround for this, and thus always put food, cloth, and leather in normal stockpiles. I use QSPs for almost everything else.
I consider QSPs absolutely essential for loose stone and ore, and also logs. I either restrict feeder stockpile size (for logs) or change the number of wheelbarrows in the feeder stockpile (for stone) to prevent it from taking up too much hauler labor until I can afford it. A 5 wheelbarrow stone QSP can take up about 10 dwarves time when working at full speed. 5 fetching stone, and another 5 or so throwing it in the cart. Several such stockpiles can use up all your idlers real quick. It can also put all the loose stone and ore in your fortress 1 tile from your mason shops or smelters shockingly quickly.
Other good uses are bars, putting all the metal and coal next to your forges, a compact furniture stockpile, a compact block stockpile in the corner of the stairwell at z-1, for quick building of aboveground structures, and many many more.
For certain situations, like moving a lot of ore from the surface to the magma sea (iron, flux, and coal all tend to be shallow), or moving the finished metal goods back, it may be worthwhile to use a moving cart, guided, to operate a quantum stockpile. This is significantly more complicated, and it can be a pain to get them connected right, but they can be well worth it. Guided carts will happily pass each other on tracks, so you can make a large number of routes using the same track that goes to everywhere, or make a large number of separate ore moving routes hooked to the same feeder stockpile in the magnetite cluster if you are dissatisfied with the speed (you will be, if you're trying to move ore from the surface down 100ish z levels with just one cart). I have had some injuries, including instantaneous pulping of upper bodies from use of carts (yes, guided, no, I don't know what happened), so try to keep other dwarves off the tracks if you have moving carts.