Most of the data comes from satellite observation. The US does have a very high density of RADAR as well. Sounding balloons and fixed weather stations are the traditional inputs. There is no explicit historical data, though arguably it is present in the use of particular schemes (weather speak for: we tweaked these magic numbers in the model so it gave good forecasts).

You can easily run WRF with the NOAA GFS as initial conditions, it would easily run on an iPhone computationally, but practically it will work on your desktop Linux box.

http://www2.mmm.ucar.edu/wrf/users/supports/tutorial.html

They have a containerized version too, which will save much fiddling with compilers and libraries.

https://github.com/NCAR/container-wrf/