FHFA (the Federal Housing Finance Agency, regulator of Fannie Mae and Freddie Mac) publishes the FHFA House Price Index. Required by law, it began in 1995 with OFHEO (FHFA's predecessor). It measures average price change for repeat sales of the same single-family homes from 100M+ Fannie Mae and Freddie Mac records back to 1975. The flagship Purchase-Only series tracks conforming purchases with seasonal adjustment; levels alone mean little and only changes count.
It is nominal, not inflation-adjusted, and does not track rents. It is neither mean nor median price: each home is matched to its own prior sale.