IMPORTANT: Structures (even containers) you build on unclaimed land decay over time and will disappear on you! I learned this the hard way. I lost my first smelter and don't have enough iron to make another one. You don't have to learn this the hard way! Claim your land! Trust me, that first 500s is better spent claiming your land rather than building a mine and smelter that can (and probably will) *poof* on you one night with no warning. Decay ticks are
very random.
And to the point above, yes you can and
should claim the land your mine is on. You can have multiple (unlimited?) claims but only one homestead.
If all you want is iron, then ardjun is correct. Build next to lime and haul the ore to your base. You've got to do
something while those smelters run, right?

People that think ore is more important than lime must live next to lime, or may not have read
the wiki very well.
Now if you want high purity iron that's a different game altogether. I'm not experienced with this, but what I understand is that the higher purity your dowsing rod the higher purity mine sites you are able to find. You grind your way up by building a mine, getting two bars of a higher purity, making a new dowsing rod, rinse and repeat.
If the above understanding is correct then I would assume you would need a smelting camp with an alt you can transfer the ore to, have it smelted and turned into dowsing rods to continue your quest.
Also, due to the above it's pretty common to find abandoned mines all over with a single boulder dug out in them. If getting the 8 nails is a problem for you then you can always pop a squat on one of those. That's how I got my fist one

My advice: buy a dowsing rod (or steal one from an abandoned town / mine, that's how I got mine), learn Prospecting, then set out. You're looking for good lime deposits. Once you find a good lime quarry then pull out your dowsing rod and find the closest mine site you can find. If the distance between the two is acceptable to you, claim land next to the lime and also over the mine. If you're trying to be thrifty on your claims, claim the mine area and haul your lime on a sled.
Note that you can fill urns or chests with chipped lime, then load four of those onto the sled. Don't haul the lime boulders. They only produce 5 lime stones. An urn can hold 14.