The Nomad house you have to collect so many antiquities. 100 or 150 if I remember correctly. The rest you have to defeat a certain number of their enemy mob. Like if you want the Hoods house you have to defeat those rival gang members. You can google a guide to Mirage apartments and get the specifics. I remember using one back when Mirage first came out.
You need faction badges, which are earned by defeating certain mobs. Here's a guide you can use to help you earn the particular apartment you've got your eye on.
Alia Misthaven