Best minecraft mining system?

I don't know wtf all this is. Just dig down in a staircase pattern

The are all equally effective.

Diagonal mining takes too much work and is inefficient.

The zig zag is silly and keeping up with where you are is tedious. Ditto pinwheel and square mining.

Try this:

Dig a long tunnel at level 5 (feet on 5). You don't have to do a long tunnel all at once--you can lengthen it as you go. Every 6 blocks*, branch to the right and to the left and dig relatively long tunnels (I like 51 blocks**). Dig a tunnel as you go that is parallel to the main tunnel to connect the ends of all the side tunnels. This will form two parallel ladder patterns. Work around lakes and lava as you discover them, but try to keep the ladder pattern.

When your main tunnel is as long as you want to go, then climb your stairs up three blocks. Shift your ladder grid by one block to make that level staggered relative to the level below. Mine your ladders pattern. Then go up 3 more blocks, stagger, and repeat. You should be at level 11. After you are through at this level, quit going up because there will be no more diamonds.

*If you space your side tunnels with 5 unmined blocks between them, you will catch all the iron and coal. You will also get most of the diamonds. Any closer (like every 3, will get 100% of the diamonds, but at the cost of a lot of wasted digging, no extra iron or coal, and a lot of diamond axes.

**I like 51 because your pick will reach out 5 blocks (times 10) plus 1 extra to form the back access shaft.