Having a furnace will allow you to smelt any ore you come across (e.g., iron or gold), meaning you can make a conceptually unlimited number of pickaxes.
The more ground you cover, the more likely you are to come across diamonds. Branch mining involves digging down to a Y coordinate of between 16 and 5, setting up a home base, and mining in two-by-two tunnels in each horizontal direction. Prepare your inventory for branch mining.
