Are there hard and fast rules about which interpolation methods are suited to each kind of raster data?
Answer
I agree there are no hard and fast rules, but there are some guidelines for various interpolation methods. For example, IDW is best when you have fairly dense points to begin with. Kriging is processor intensive, usually used in soil/geology modelling. Spline is usually used when a smooth surface is desired, e. g. temperature data Some methods keep the resulting raster passing through the original points while others do not.
Although it is ArcGIS centric, a good overview of the different methods can be found in the 4 page paper
Interpolating Surfaces in ArcGIS Spatial Analyst
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