During your first night you should probably mine like I said before but maybe you want to know a few tips...
The Jungle has the best caves but most dangerous so don't go there till you have the right gear.
Snow caves are so so but they do sometimes have good loot.
Normal caves are somewhere in between but are useful for the first night.In the caves try and get some Iron, Silver and if you can find any Gold. These minerals are the basis of any good world. While your down there look for some chests and heart crystals.
The mining aspect of terraria is kinda boring sometimes but you have to do it.
Happy Mining...........
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A guide to Terraria iOS
Non-FictionThis is a guide to Terraria if you have no idea what the heck that is well you might as well read the book