Why go to all that trouble for a slime rod/binding when it'll be obsolete once you get iron?As beginners pickaxe I recommend a blue slime tool rod and a blue slime tool binding with a stone pickaxe head.
To get the slime balls, kill a bat, morph into it, fly to a slime island and profit ;D
You can repair it with cobble AND it's got high durability.
Here's a beginner's pick: explore until you find a village with a blacksmith's house that contains a steel item. Put the item in a smeltery, use it to make a steel pick head. Now you can mine cobalt and ardite without having to bother with anything else.