My technique for quarry mining is pretty different to most people.
1. Dig a 3x3 hole at the surface.
2. Quarry down to layer 60, placing ladders/vines as you go.
3. When you reach layer 60, expand the original 3x3 into a larger 16x16. Make sure the entire 16x16 is within one chunk, so you don’t miss any diamond ore generated in it (only up to one vein of diamond ore can generate per chunk). You can use the F3 debug screen to see which chunk you are in.
4. Once you’ve opened up the 16x16 at layer 60, start by digging 2x2 holes all over it. Leaving a border of 1 block on every side, dig 2x2 holes with a spacing of one block between them. The end result should be a 5x5 matrix of 2x2 holes, with 1 block borders running between all of them. This will minimise your digging while ensuring you don’t miss any ores.
5. For every one of your 2x2 holes, quarry down to bedrock, one by one, placing ladders along the way.
BONUS: if you want, you can also convert this into a regular mine once you’re done with the original quarry (This will only work if your ladders/vines occupy only one block column.). Going down any one of your 2x2 quarries, go to layer y=11, and build a small, 3 block platform, with one space for the ladder going down from layer 11 to bedrock. Break a 1x2 opening between all your 2x2 quarries at layer 11, doing the same 3 block platform for all of them. Once you’ve built all the platforms and connected all your quarries at layer 11, go to each side of the entire 16x16 chunk and start mining out a tunnel from all 4 sides. From there you can start regular mining. You can even do a pinwheel mine if you want - branch out sideways from every one of the four tunnels you made at regular intervals. Since you started out from a square, if you dig a branch to the right from your north tunnel and branch to the left from your east tunnel, they will eventually meet at a right angle. If you really want to be efficient with that kind, space all your branches from the original four tunnels at intervals of 2 to 3. This will make it impossible to miss any ore at that layer. Also if you didn’t know, I suggested layer 11 because that is the optimum layer for branch mining. It allows you to avoid the lava lakes at layer 10, while allowing you to spot diamonds on y=12. Don’t forget a water bucket though, because if you come across a lava lake, although it won’t be right in your face or your feet, it will be below you (since the block below you is y=10). Hence you’ll need a water bucket to neutralise whatever lava lakes you come across.
To conclude, quarry mines aren’t as bad as people think because they can serve lots of purposes. If you use the more common method of digging out the entire 16x16 area instead of using 25 separate 2x2 quarries, you can use the bottom bedrock layer as a mob farm since any mob spawn attempts at that layer will all spawn within the 16x16 area (provided there are no caves nearby). Just remember to put a ceiling on top or the spawn attempts may fail in daytime.
Hope that helps!