If you are not planning to use a statistical method (which would be preferable) I would use Natural Neighbor interpolation rather than IDW.  Natural neighbor interpolation is 100% determined by the geometric configuration of the sampling locations and as such requires no arbitrary choices, with the exception of how to control extrapolation beyond the convex hull of the sampling locations.  

If you are committed to IDW, I would recommend a cross validation analysis to select the neighborhood parameters.  I would also select a range of them and look at the resultant map so you can see what these choices do in practice.  Generally IDW promotes relatively extreme spikiness in the data that is unnatural and frequently defies intuition.

Also if you are open to alternative methods I would compare them through cross validation as well.

Sibson, R. (1981). "A brief description of natural neighbor interpolation (Chapter 2)". In V. Barnett. Interpreting Multivariate Data. Chichester: John Wiley. pp. 21–36.

As a university student you probably have access to an implementation of this method in R or MATLAB.  

I would also look at the PRISM model of precipitation which is a spatially and geographically informed interpolation of rain gauge data that I have found to be quite accurate in the Western United States.

Thanks John and Jayshri for your responses. Jayshri, what you describe is what I have been doing so it's good to know you'd agree with my methods of experimentation. 

I agree with Jayshri, but you have to take under consideration the topography as well.

I don't know anything about rain gauge data, but I guess its variation reflect, at least to some level, the locality effect. In that case you might try to use more stochastic approach such as Kriging (which is also available in ArcGIS.With this model the interpolation will be based on the data spatial variation itself, instead of just spatial proximity which is,  as John mentioned sometime defies intuition. 

Another suggestion, just to check the effect of any topographical factors (elevation, temperature etc) you might want to try using Geographic Weighted Regression (GWR, which is, again, available in ArcGIS) and then try to cluster the whole area based on factors that are found to be significant (if any). That will, hopefully,  provide more empirical base to your result.     

Good luck....

Hi,

I would, just like Mr. Pramono and Mr. Kern also recommend geostatistics. If you can get hands on a DEM of the area (SRTM or Aster is free), you could perform regression kriging and use the DEM for an estimation of precipitation variation with height above the sea level. Then you could use kriging to interpolate the residuals and add that to your linear model.

regards