When you go mining in Minecraft, the most important things that are necessary are: torches ,sword,pickaxe,armour(maybe),wood,furnace(maybe you could craft a furnace while your in the mine) ,crafting table (same as for the furnace) and a map (only if you are playing on anything other than pc). Remember for different ores there are different pickaxes needed:
Coal -wooden and better
Iron-stone and better
Gold-Iron and better
Redstone-Iron and better
Lapis lazuli-Iron and better
Diamond-Iron and better
Emerald-Iron and better
Nether Quartz-Iron and better
As well as that, the different ores are found at different heights ,to know which height you're on you have to look on a map (if you are on pc then hit F3):
Coal-found on the surface and below
Iron-0-67
Gold-0-35
Redstone-1-19
Lapis Lazuli-19-32
Diamond-2-17
Emerald-4-31
Nether Quartz-Spawns naturally in the nether.
While mining if you come across a dungeon or a mine shaft you are very lucky! They can have chests with useful items(but be careful the will also have mob spawners).
No 1 rule in Minecraft
Never dig straight down (or straight up) because lava might fall on you or gravel might fall on you.Most people think that with a fire resistance potion you are safe. But you are not gravel might fall on you or if you dig into an underground ravine you will die of fall damage,so yeah keep that in min 'e' .ha ha get it? Mine instead of mind? It doesn't matter. Useful tip: Lava isn't baked beans so don't jump in to it. Plus why would you jump in baked beans.