How good are we at telling a far-off asteroid's composition? That would seem to be the crucial thing to me. You'd need to hit upon an asteroid made of seriously valuable stuff to be able to cart back enough minerals to make the mission commercially viable. I guess beyond that there's the issue of whether you could safely fly into what would probably be an asteroid field.
The easiest way to do so from a distance would probably be an impact probe - kick up enough debris and you can aim a spectrometer at it and figure out roughly what elements it has. But you aren't really going to know what it's really like (on the level of chipping/zapping away at it) until you get there, which is a big problem for automated equipment especially. I personally think the Moon would be a safer bet - craters mean asteroids live there already, after all, and it would eventually provide an excellent base for launching further mining efforts towards NEOs and eventually the belt.
True, but the safest bet to get to the Moon would have been to build some kind of space station first, *then* go to the Moon. Back in '69, we said "Fuck it," and went straight to the moon with no support infrastructure. That's the kind of leap forward we need, IMHO. We need someone to figure out the logistical and technical hurdles and say, "Moon? Mars? Screw that, we're going to the Belt and coming back with a mountain of gold, baby."
I live for the day when James Cameron personally pilots some kind of glorified space tug hauling a rock back with enough rare-Earths and isotopes in it to be worth the GDP of a moderately-sized nation. 'Cause I can guarantee you the 2nd Space Race would be ON.
Will it happen? Highly unlikely, at least in Cameron's lifetime. But it's worth pinning some hopes on.