The renewable resource page on the Minecraft Wiki is a great help.
I did something like this on an adventure map ("Land Claster" or something like that) where you're thrown onto a floating island and there are a half dozen others you can build towards. I might recommend a pre-made adventure map like this so you can learn by experience.
As far as what you need to build stuff versus living in a cave; the easiest renewable building material is wood. You need dirt to grow it, but you never consume it. Metals, strictly speaking, are renewable, but you can only get gold from Zombie Pigmen (in the nether), and iron from killing (personally, mob grinders don't work unless they just weaken them) Zombies. In order to get into the nether to get gold you'll need lava, water and diamond (or loose blocks of obsidian). Lava and water can also be combined in a cobblestone generator to create infinite amounts of stone (using a slightly less infinite amount of wood).
Animals yes, and you'll want some grass to feed the sheep and be able to use bone-meal to force some tall grass to get wheat seeds or flowers. Bone meal is free; almost too easy in a sky map with limited spawn space; you'll be rolling in it once you get a grinder going, along with tons of absolutely useless gunpowder.
Sand/glass is another non-renewable resource, along with other minerals; gravel, redstone, lapis lazuli, etc. "Coal" proper isn't renewable, but you can make the next best thing; charcoal, endlessly with your tree farm.