Well, seeing as how most of the 1st world has either seen or heard of the Matrix, it's not likely that we could without having a major military advantage...and then there's the issue of a bunch of Neo-wannabes...
BTW, I've finished the plans for the partial asteroid base. Basically, it would be a wheel spinning around a dense core at an uncertain speed, maintaining a good amount of gravity (usually a bit above 1 G). Also, there's a higher-gravity gymnasium/barracks/training center thingy, and facilities for mining stuff (presumably mining drones of some sort--I haven't figured the specifics out). I'll add a bit of class and readability, as much as I can with all of the notes scattered about, and then figure out a way to post it. BTW, it's not intended to hold more than around a thousand people (military, miners, technicians, medics, officers, etc), and while it DOES have a few weapons, they're not much or detailed and are primarily intended for point defense, so another base (probably on Mars, given the poll's results, although Luna's not an impossibility) will be needed.
Here's an idea:
--Mars: Our main base. Will possibly export some food, although all bases should be able to sustain themselves for a while.
--Luna: A staging point for the Terran war. Probably a couple thousand people, mainly guards and war-machine operators; also some kind of big Gauss cannon, solar generators, etc. Most of our warships will probably be put into Lunar orbit. Also make sure to put some farms and solar generators up!
--Asteroid belt: At least one big base, the D.W.A.R.F. I've designed, would be nice--training soldiers far away from the Terran forces and mining at the same time! Some food processing/agriculture/etc has been included on my design, but some food will probably be needed to be imported. This will be compensated for by being able to mine. Also, the asteroidal base will probably need a fair bit more electricity than can be obtained by coating its surface with photovoltaic cells; I've accounted for that in part by suggesting such things as generators in the exercise equipment, but a fair amount of mining of uranium and the like would be needed. Perhaps some smaller base will be set up on Ceres or something, to store the ore and such; this would likely be a small settlement.
--Spaceships: Not too much more than you see in harder sci-fi. The big issues will be gravity and power; I suspect that centrifuges and nuclear power will be the solutions. There would be a fair number of warships, primarily focused on taking down Terran warships before they can damage us and perhaps some with orbital bombardment, in case the Gauss cannons don't work. Most ships, however, would probably be various sorts of freighters, moving gear, people, and minerals around the solar system.
Thoughts?