Just my 2 cents, but a vacuum isn't an advantage it's a disadvantage. It's hard to work in a vacuum - humans need to wear bulky suits and humans are still often needed for set up and repair. Also pistons that rely on fluid would need to be air tight. Space is also full of the occasional cosmic ray and solar storm, so it's not an easy place to work.
I'm not sure micro-gravity is much of an advantage either. It's hard to work if the slightest force propels you away from the object you're trying to work on. Low gravity could well be an advantage, but micro-gravity - I think that's a disadvantage.
OK, that out of the way, there's no shortage on what they would mine if asteroid mining was cost effective - Wiki has a page on it. http://en.wikipedia.org/wiki/Asteroid_mining#Financial_feasibility
But the issue is 2 fold. 1) cost and 2) guaranteed return.
Wiki makes the point that one particular asteroid
"16 Psyche is believed to contain $1.7×10^{19}$ kg of nickel–iron, which
could supply the world production requirement for several million
years"
When we mine iron on earth, we dig through thousands of tons a day. The trucks alone are as big as a small building and the factories that melt and separate the minerals from the earth - enormous. To do asteroid mining, you have to try to minimize the equipment needed cause launching things in space is very expensive. If it takes 100 years or longer to get equal return on investment - that's not attractive to an average business cause they get killed on interest payments alone.
So it's a fun idea, but, for now at least, not practical. I mean, if one company gets an asteroid and a million year supply of Iron - what's to stop a 2nd company from, 20 years later, doing the same thing but with better technology - that leaves the first company holding a big loss.
The real trick with space mining is to get the technology to send something in space that can build machines in space - and while that might sound terminatorish, that's really not what I mean. What I mean is, you can't send drilling equipment up to an asteroid the size of Wyoming, what you need to do is send equipment up to Wyoming sized asteroid that can build drilling equipment from the asteroid material, so you can increase production quickly. Right now, we don't have that technology. It's similar to the Mars problem. What we really need is the ability to build things fairly quickly on Mars if we're going to settle there and right now, we don't have the means to do that. Setting up a colony on Mars with today's tech would be very slow, and probobly would lead to the death of the colonists.
on Today's tech, it's very hard to see how the benefits would outweigh the costs for asteroid mining especially since the process can be copied by someone else the instant it becomes profitable and the tech is improved.
But long term, the benefits of mining something as simple as Iron in space is obvious - because ultimately, it's more energy efficient and cost effective to build things in space than to keep sending stuff from earth into space. . . .but we're not there yet technology wise. How long it will take for that to happen, that's hard to say, but at some point, with improving technology, I think it's sure to happen, and when it does, mining for basic stuff (Iron, water, nitrogen, carbon, oxygen) and for more exotic stuff (Platinum, Iridium, etc) and possibly helium, which we don't think of as valuable, but it could become valuable if Fusion ever gets figured out. I'm sure it will make sense eventually, but perhaps, mostly not to send back to earth, but for building stuff in space.
at least, that's my thinking on the subject.