OK, my 2c: For efficient storage of stone and logs you can't use some kind of container since they are too "big", and maybe we can solve a lot of problems at once here.
THE IDEA
The idea is to have a silo of some kind. This would involve a multi z-level structure to be channeled out, with an inlet in its roof, and some kind of outlet at the bottom, with a hopper made of ramps to guide materials out. I think a good way to acomplish this is to be able to designate an area next to a hole in the ground either as a special zone or kind of stockpile*.
THE MECHANICS
Items dropped into the hole in the ground fall directly downwards. Tiles have a volume limit they can hold, and when overburdened will relieve themselves in one of the 8 adjacent squares to the sides or above to one of the 8 diagonals or upwards,preferentially to tiles on the same z-level. Some kind of mechanism then exists on the floor tile of the hopper to dispense singular elements from inside the silo area to the tile directly below. A properly designed hopper (ramps converging on 1 tile) is needed to completely empty the silo from the ouside. This would also require (certain) items to be able to roll down ramps.
THE DETAILS
In the best world the holding capacity of a block should be based on the approximate volume and geometry of the contents**. This required knowledge of the packing of spheres and cyllinders - for cyllinders the highest achievable packing density is ~0.9. The densest achievable packing of spheres is about 0.74 - this is for carefully packed, maximally dense materials, but "if yer just roll the logs in facin' teh same way, then they kinda fall like tha' ey?", and we can assume the dwarves, natural masters of stone, can achieve optimally dense packing by just throwing rocks in. Given that things already have volumes, this should give a good starting point for the carrying capacity of an in game square, and with silo zones as described above, youre in business for throwing just about anything in a silo.
Alternatively, this could be approached from a more game-oriented perspective, and decide what a reasonable amount of stone and logs are to hold in one square. limiting the use of silos to these otherwise containerless substances. My gut says about 5 stone per 1x1x1 volume, and though I instinctively want to say a bit more for the wood, I think that's a pretty solid number for logs too, gameplay wise. That means a 3x3x2 space with a hopper would look like so:
|1 2 3|
|1 2 3|
\ 1 /
And have a volume of 9 + 9 + 1 + 0.5 *4 + 0.25 * 4 = 22 squares, and be able to hold 110 stones. An equivalent 3 level stockpile with the hopper ramps mined out would be able to hold 27 stone.
THE IMPACT
In some senses, pretty massive. This would completely break quantum stockpiling, and dumping stone down a shaft wil eventually fill up. There is also the interesting question that if a stone can walk on 5 stones, can a dwarf walk on a tile to a z-level above if that tile contains 5 stone? Sounds like it could have consequences.
I think this is a superior solution for stone and wood to another container, as it opens the door for other cool things - minecarts autofilling from a hopper at a minecart stop, before being bumped on the road by the next cart, for an automatic matter transport system? Being able to dispence individual stones for your masons from a neat silo? Accidentally throwing some logs in your stone silo and having your masons flood the workshop with logs waiting to get a stone from a designated stone dispenser? Losing an idiot that opened the side-door to the silo and was pulped by a flood of stones? Does this limit the amount of water that can enter an area? Can you dump an entire silo of stones down a ramp into a pond to flood the surrounding area? So many enemies falling into your lavamoat that it overflows?
Truly, these are dangerous !!FUN!! times.
* A zone has the mechanics to dump, but a stockpile has item filtering, which would be needed. Perhaps some mutant bastard where the zone indicates you dump into the hole, but the stockpile inside it filters what goes in... but I wouldn't recommend it. Hacky solutions bite you in the anus.
**This is simple for logs and stone, but becomes laborious for equipment, so my suggestion would be to preliminarly exclude equipment from tile capacity calculations.
Example of a tile overfilling. A simple model would be to have a tile have a maximum capacity and when reached, send off excess in one of the other directions, but it would be significantly more fun to have a tile have a max of eg. 3 unless it's neighbors all have 3, at which point it can increase to 5, to simulate heaps forming.
TOP VIEW, middle tile heavily overfull, spreading to neighboring tiles, overfilling bottom right, which pops a stone in a random direction.
+++++ +++++ +++++
+++++ +OOO+ +OOO+
++O++ -> +OOO+ -> +OOO+
+++O+ +OOO+ +OOOO
+++++ +++++ +++++
SIDE VIEW: Stone enters silo with properly designed hopper, falling on other stone.
|| | | |
|v | | |
| | -> |O |
|OOOOOOOO| |OOOOOOOO|
\OOOOOO/ \OOOOOO/
\OOOO/ \OOOO/
\OO/ \OO/