Coal can generate from Y-level 0, up until Y-level 256. Coal generation is affected by air exposure below Y-level 136, which means caves will not be a good source for coal in lower levels.

Gold can generate from Y-level -64, up until 256 but, Gold can only generate between Y-level 32 and 256 in the Badlands Biome. If you are searching in other biomes, for best results, you can search at Y-level 32, -64, and -16.

Lapis can generate from Y-level -64, up until Y-level 64 but usually in small amounts. For best results, search at Y-level 0. (Strip mining will help).

Diamond can generate from Y-level -64, up until Y-level 16. For best results, you should mine at Y-level -58

Copper can generate from Y-level -16, up until Y-level 112. Copper generation is significantly increased in dropstone caves. For best results, you should mine at Y-level 48.

Emerald can generate from Y-level -16, up until 256 but, they will only generate in Mountain Biomes. For best results, you should mine between Y-level 224 and 256 in a Mountain Biome, where emeralds generate evenly.

Redstone can generate from Y-level -64, up until Y-level 16, just like Diamonds. For best results, search at Y-level -58.

Iron can generate from Y-level -64, up until 256 if there is land there to support it. For best results, either search high at Y-level 232 or low at Y-level 16.