Here's the basic outline of how to buy the villa... and the 'walkthrough' more or less.
1. Focus on getting established in Rome. In the beginning your best source of cash is not the bordello, it's trying law cases at the basilica.
2. Be sure to improve your stats - rhetoric, etc
3. Initially buy only Fasti and train her until she can open the bordello. Repeat this for her multiple sex / non-sex acts. Once she's more or less fully trained, buy Parmida. repeat this process for Parmida. Repeat for Inga.
4. Socialize at least a few times in the Baths.
5. Get Alfidia trained with Valeria
6. Upgrade the bordello at least one step
7. Talk to Charis a few times
8. Talk to the furnisher, the labor merchant, and the remote merchants. One of them will tell you about buying a villa.
9. Go through the hoops at the Basilica to buy the villa, it takes time.
10. Hire the villa manager - talk to merchants again
11. Set the villa manager to 'stay' at the villa.
12. Now you will get the upgrade quests from the villa manager and Charis when you talk to them
13. That's about the extent of the last release. In this next release there will be more quest activity after this.