This depends on the NEO.
One will, of course, choose one with a satisfactory orbit relative to earth - most definitely NOT a distant/fast/etc one with launch windows years or decades apart.
If you choose an asteroid whose orbit is substantially different than earth's you pay a delta V penalty.
If you choose an asteroid whose orbit is like earth's you have rare launch windows.
Launch windows open each synodic period. Synodic period can be found by (period 1 *period 2) / |(period 1 - period 2)|.
Let's say we have an asteroid with a very earth like orbit whose period is 1.1 years. Earth's orbital period is 1 year, of course.
(1.1 * 1) / (1.1 - 1) = 1.1 / .1 = 11.
So the synodic period will be 11 years.
As a general rule, the lower the delta V, the rarer the launch windows.
And yet, you can still find NEOs with very convenient delta vs and launch windows.
For example:
http://en.wikipedia.org/wiki/4660_Nereus
If you are actually serious about mining asteroids and shipping part of the ore to earth, you won't care about a few extra tonnes.
This means you send humans, not robots.
Humans in habs (aka
canned meat) add enormously to difficulty and expense of a mission.
Given existing paradigms, there's no way mining asteroids could enjoy a return on investment.
About canned meat - I'm not talking about building an interstellar ship (as in your link), but a stationary O'Neill colony; you can make it as massive as you like without worrying about getting it to move at any velocity.
And this mass should not come from earth - rather, it should come from the asteroids; from earth, you'll only need to lift the mass necessary to keep the miners alive during the trip - so 'a few extra tonnes',
sojourner.
Yes, human beings require life support systems - which can be, for the most part (oxygen, centrifugal gravity, etc), artificially/technologically generated - and solar power can provide all the energy you need in the solar system.
They need food, which you have to grow, at least in the long term - again, light from the sun giving you the necessary energy for plant growth.
We already know how to build huge, light mirrors to collect/focus solar light; we call them solar sails.
The only problem we don't know how to solve - as in, it's not, basically, XIX century physics/chemistry - is cheap access to LEO.
And without this, there will be no return on investment - or, rather, you'll have to wait for some time before you receive your return on investment (until slow moving shipments of ore reach earth).
It should be noted, though, that there are many proposals on how to overcome this problem - and many are very convincing.