The Mining skill is used for Ores, Essence and gems. To start mining no requirements are needed.
Upgrading your pickaxe should be done whenever you have the possibility to. The upgrades are available in the shop Pickaxes.
Mining offers two alternative Gloves. Which can be found in the Gloves shop.
Mining > Runecrafting & Smithing
This way opens up the option to go for Smithing & Runecrafting afterwards. As you are leveling up your mining once done you can continue smithing and runecrafting. The key here is to get money for gem gloves. So a advice is to get 500k to purchase Gem Gloves. Some sort of moneymaking is adviced to reach this. If need of money sell all gems to rebuy gloves. Diamonds are useful for late game however they can easily be stocked up later in the game.
1-15 Copper/Tin ore
Mine either tin or copper.
15-30 Iron ore
Mine iron until you unlock Coal.
30-50 Coal ore
Mine coal until you unlock Mithril. All coal will be needed for the smithing grind.
50-99 Mithril ore
From here on the mission is to mine Mithril with Gem Gloves all the way.
Once 99 Mining is achieved you unlock the Mining Skillcape. This gives 1 Coal ore for each ore mined.
With the Skillcape equipped you have to mine about 330K essence for 99 Runecrafting. The gem gloves does not work with Essence. If affordable the Mining Gloves are a good way to speed up.
99 Coal ore
After you are done you will still need about 235k coal ore. Gem gloves are still recommended.