You'll have to speak to @
Barbasol about that, but as far as I know, new citizens get a room in the gatehouse tower barracks where they can store stuff. Once the trial period is over (I don't have any details on that either) you can apply for a plot in the undercity or on the surface when we make them available. Conditions on getting a plot and building regulations are not yet set, since the undercity is still pending some finishing touches.
For a guided visit to the city you can ask barbasol, me or another manager you find online. Bear in mind the city is under heavy construction work for now, and a lot of things are a bit messy and improvable. Still the interior of the gatehouse tower and the spire staircase are secure grounds.