A few things I made (sorry, no pictures):
In one testing fort I decided to build the fort between the magma sea and the third level caverns,
but I also wanted easy access to the surface. The biggest problem was moving trade goods up and wood
and plants down. This was solved by pairing a drop shaft with a impulse elevator.
Minecarts and items were fed into the drop shaft at the top and separated at the bottom by sorters.
Minecarts going to the bottom of the impulse elevator and items going to a small stockpile that was
right beside the main stockpile level. The minecarts were placed on a track that lead to an automated
loader that filled them with trade goods and other items that needed to go to the surface (like seeds).
Since I had sorters at the bottom I did not have to worry about filling carts at the top, the empties
just went directly to the drop shaft.
Dwarves would fill stockpiles at the top of stuff to go down, this stuff was fed into the drop shaft
via quantum stockpile like minecart setups, at the bottom the "going up" stockpile and the "just
arrived" stockpiles were right beside the main quantum stockpiles, making final storage easy.
This was built before I made conveyor belts, so I used sorters for moving items around (away from
the drop shaft bottom and the like), with belts this would be even easier to build.
In another fort I solved the problem of cage trapped invaders by making a 100+ z-level drop shaft.
Anyone who has ever made such a drop shaft knows that they have one major problem: you need to seal
the bottom to keep your dwarves out so that no one gets crushed by a falling goblin. This means that
you need to run the system in cycles, drop a few creatures then open the bottom for cleaning, repeat.
This gets tedious in a hurry.
I covered the bottom of the shaft in conveyor belts, so exploded creature parts would get swept off
to a minecart loader for transport to my main refuse stockpile. Simple, efficient, and fast.