Hi Clark,
Well first of all the order in which you stack the media is highly dependent on the waters's flow path through that particular filter so I'll just describe the reasoning in general terms:
Water entering the filter for the first time is generally "pre-filtered" by the coarse sponges to remove the large debris which endangers the biological filtration process due to possible clogging. Since the coarse sponges are usually easy to remove and clean this makes sense.
The next size debris/detritus is suspended in the water and is small enough to pass through the course filter. This is like silt in a river. Fast flow carries the suspended silt, so in order to get it out of suspension the idea is to slow the flow down and the lower flow energy drops the silt out of solution. This is the job of the noodles/rings. If this wasn't done the silt would carry into the biological media and clog the pores of the media, reducing the available surface area for bacteria to colonize.
The water then enters the bio and/or chemical areas mostly silt free. Bio/chemical filtration is accomplished and the las remaing sponge/wool is finer than the coarse sponge and traps the very fine particles that neither the coarse sponge or the noodles captured. I suppose one could argue that this ought to be placed before the bio media to give added protection to the bio-media so I guess this counts as an option.
Again, this is just the basic architecture, nothing revolutionary really, so just think about the direction of flow through your particular filter and adjust accordingly. Yes, some biofiltration does occur in all sponges, wool and noodles and yes, the bio-media does trap some silt/detritus but that's just how it goes, and that's why regular filter maintenance is important.
Cheers,