new to the game with a few questions

[Niwashi]

Housing: There are housing districts in each major city - they are not instanced, there are wards with a set amount of plots, but on many servers there are absolutely no plots available. or no small/medium. If your server is populated, you're probably out of luck until they add more wards.

Prices for your server listed (Diabolos) BEFORE price reduction over time: Small plots are 4-5mil, medium are 30-37mil, and large are 70-87mil. They aren't cheap.

Wards: The Lavender Beds - accessed from Central Shroud docks; The Goblet - accessed from outside the Ul'dah Gate of the Sultana (Western Thanalan); Mist - accessed near Red Rooster Stead in Lower La Noscea.

To get a personal house, you also need to be at least level 50 and at least a Second Lieutenant in your Grand Company (which is currently max rank, though I think more ranks are being added in the expansion).

To buy an FC house, the FC needs to have reached Rank 6.

[Edit (thanks for the correction, Conradus)]:
If your FC has a house, I believe the only requirement for buying a personal room within that FC house is that the FC leader needs to allow it for you in the FC's permissions settings.
If your FC has a house, in order to buy a personal room within that FC house, you need to be at least level 50 and a 2nd Lt. in your Grand Company, and the FC leader needs to allow it for you in the FC's permissions settings.