So if you are 15 Mining, the best pickaxe you can wear is Black pickaxe, but the steel pickaxe is easier to get, however, you can buy both of them from the GE. At level 21 Mining, you can wield the Mithril pickaxe, wield Adamant pickaxe at level 31, and wield Rune pickaxe at level 41 which is the best pickaxe in F2P.
To expedite this, I would highly recommend completing Doric's Quest and The Digsite, which grants the player a total of 16,600 Mining experience, elevating Level 1 Mining to Level 32. Both quests have fairly low requirements, and completing them allows the player to skip early levels and use Adamant pickaxe right from the start.
The Adamantite Pickaxe is the fourth-highest tier pickaxe as of 1.2, being one tier above the Orichalcum Pickaxe, but one tier below the Chlorophyte Pickaxe. It is surpassed by its alternative version, the Titanium Pickaxe. It is able to mine any block except Chlorophyte Ore and Lihzahrd Bricks. v1.2 Added to the game.