No you don't have to pay real money to buy a house. Some people will buy housing lots and will then sell the plot to some one for how ever much (I've seen some people trying to sell plots for around 6 mil Gil before) if you buy the plot from that person they go and give up the plot then you can buy the plot for what the game lists it for.

If you hold out and keep an eye on the residential areas you will find plots pop up, it's just a waiting game. For a small house I would suggest having about 3-4 mil Gil on hand so when a plot comes available you can run and grab it before someone else does