I believe that gold spawns under level 32. And Iron under about layer 64. But if I were you I would strip mine a level 12 because you can also find diamonds and redstone.As for resources being more common in mountain biomes i do not believe that this is true.
There is no layer where iron is most common at, same goes for coal and gold. However, there is a certain set of layers where the ores have the same rarity at. For gold it's 5-20 and iron and coal are pretty much very common on most layers.
If you want more exact answers then just go to the minecraft wiki, which I find provides enough explanation.
There are more caves in extreme hills biomes, so caving is more effective.
Cave generation is solely dependent on the world seed and chunk coordinates, with nothing in the code (which I'm very familiar with) to suggest that biomes influence cave generation; sure there may be a few more caves above sea level in mountains (cave density is much greater deeper down, peaking around layers 16-32), but you aren't going to find anything other than coal in them.
As for ores, the Wiki has a table and graph of ore distribution; note that the oft-quoted layer 11/12 for finding diamonds only has the advantage of not having lava pour into your mine; you can also mine at y=5 and find the same number, if not more, since if your feet are at layer 12 your head and the ceiling are above the most common diamond range (lava is slow enough so you can easily avoid it as long as you stand back a bit).
Also, I looked at the code for 1.7.2 (obfuscated but readable) and found that ores still generate the same way as 1.6 or earlier, so all of the figures for earlier versions are still valid (except for dirt and gravel, which are generated as "ores"; their height range was doubled to the world height limit, but they are also now half as common for the same volume of stone because they forgot to double the number of deposits generated).
I usually find that iron is most common about fifteen blocks under the surface. Call it the placebo effect, if you want, but there is something about that particular level that, to me, seems to spawn the most amount of iron ore.
Really? I'm sure I read somewhere that more caves generated in extreme hills biomes (not just above y=63), it certainly seems that way from personal experience too. Could be mistaken though I guess.
Yeah, the Wiki claims that caves are more common in Extreme Hills, but there isn't any evidence that they are more common there below normal ground level; excluding caves in mountains. I've found big cave systems in pretty much all biomes (in 1.6.x and earlier), exploring thousands of blocks of caves) and when I mod caves new cave systems appear at random; one mod might have a cave system in Extreme Hills but another won't. The biggest single cave system I ever found in vanilla was in a plains biome; in a world with the same seed but modded cave generation, taiga, with Extreme Hills nearby but only in the outermost fringes.
Also, the code itself just uses the world seed and modified chunk coordinates (multiplied by a couple random numbers derived from the world seed, then XORed with the world seed) to seed the random number generator before generating caves.
Not only that, if you generate a world with large biomes or Amplified, cave systems generate in the same locations as in a default world, despite the biomes and terrain at those coordinates being different.
According to another wiki article, iron is found at about the same amounts at levels 5- 40. However, there is a very very very small budge in the area at level 36, but barely.
Coal is found at about the same amounts at levels 5-40.
Gold is found at about the same amounts at levels 5-28.
Diamond is found at about the same amounts at levels 5-12, and there is a small budge showing that 12 is where diamonds appear most.
Since 12 is good for iron, coal and gold, and diamonds are mostly found there, and people mine with feet at 11 so lava is not a large problem since it spawns mostly at 10, so using water will create an easy obsidian floor, and with diamonds at levels 10-11 more than levels 13 and 10, if the player would mine at feet on level 12. Just want to show the info.
If you really only need iron I would just recommend caving since you can find tons of exposed iron ore in caves along with other goodies.
If you want other resources aswell strip mining might be an option but the people who posted before me gave much advice in that direction.
You can find a lot of stuff by caving; I've found hundreds of blocks worth of diamond just by exploring caves; I just found this, got 18 diamonds with Fortune III (8 ores), and I found several more veins just today for a stack of diamonds (plus lots of lapis, gold, redstone and emeralds, being in an Extreme Hills biome, not that this contradicts my last post):
Of course, it isn't a very efficient way to get diamonds; I only find about half as many diamonds relative to the ratio they generate in relative to iron, of which I mine thousands of ores on a typical trip (using a backpack mod, or Ender chest in vanilla), even though I always check to see if there is more diamond diagonal to a vein and never do this for iron (only diamond, lapis and gold; I also use a Fortune III pickaxe on everything, even coal).
Although caves were nerfed in 1.7.2, but I hacked the game to make more generate, even more than the old generation; the above screenshot is from 1.7.2, in the middle of an insane cave system, if not as insane as one I spent a couple weeks (a long time for me to spend in a single system) exploring in my 1.6.2 main survival world.
Not that you have to miss out on them; I uploaded a mod that enables you to get back the old cave generation (when MCP and the mods that I use update, I'll move my main survival world to 1.7.2, along with a very complex cave+ravine mod I made).
I tend to start my diamond hunting at level 10(foot level, not eye level), and during the process can find a good amount of other ores. In the meantime when going for iron at the get-go, I will either look for a decent cave or dig down to about level 50 and mine from there. Less chance of stumbling into lava short of falling into a chasm. Good luck!
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In the real world, you stick your head in the dirt to hide from problems.
In Minecraft, you stick your head in the dirt to find problems.