Excuse my ignorance here, but wouldn't the easiest solution of all just be both mining minerals and performing construction on the moon? Once you are established there, you pretty much have the space construction port you're looking for, do you not?
A lunar base would be very expensive in terms of initial construction because it costs so much to climb from the Earth's surface through the Earth's gravity well, and then to descend safely on to the Moon's surface.
An interesting solution that I've followed has been the proposal to send tiny self-replicating robots to the Moon and have them construct everything else from Lunar materials. See for example: http://www.islandone.org/MMSG/aasm/
This good idea was most recently promoted by Newt Gingrich during his US presidential primary campaign. My own opinion is that private investment, not government money, should be used for space-based economic projects.
A chart http://upload.wikimedia.org/wikipedia/commons/c/c9/Deltavs.s...
See: http://upload.wikimedia.org/wikipedia/commons/8/82/Orbitalal...
http://upload.wikimedia.org/wikipedia/commons/c/c9/Deltavs.s...
As you can see, getting from earth to LEO requires 9.3-10 km/s of dv, depending on the type of rocket you are using. All of this must be high-thrust propulsion, otherwise you'll immediately fall back to earth. 9.3-10 km/s of high-thrust propulsion is indeed quite costly to implement.
On the other hand, to go from the lunar surface to LEO is only 5.5 km/s of dv -- and only 1.6 km/s of this (the trip from the lunar surface to lunar orbit) needs to be under high thrust. The rest of the dv can be done with relatively inexpensive low-thrust techniques which require little or even no propellants -- such as ion propulsion, solar sails, and aerocapture.
So to a rough order of magnitude, it's 2-6 times cheaper to get to LEO from the moon than from the earth.
Edit: miscalculated the lunar surface->LEO dv requirement.