Simulating rainy weather
The problem with a statistical model is the reliance on dynamical model input, plus the requirement of climatology. A statistical model will also only give data for a solitary point, not an area. The simplest statistical model is persistence, which is the current weather, followed by climatology. Both are the lowest in forecast skill.

For a dynamic model, try using the WRF model (http://www2.mmm.ucar.edu/wrf/users/download/get_source.html).

It is a commonly used model. The runtime will range, depending on your computational power and needs. A larger domain will take longer, and require more. I know people who simulate hurricanes with it, and people who run fine scale modeling.

I can run WRF with a 200 km domain size for a 36 hour forecast in 1-2 hours.

Again it will really depend on your resources. Running WRF may require compilers you do not have access to. You can develop the visualization software after you ran the model, with whatever tools you find. Python and NCL are good languages, but MATLAB and a variety of other languages can be used.