I'm performing a cost distance route selection analysis for a type of linear infrastructure in Australia. The process I will use will be similar to this ESRI tutorial. The route will traverse several states and therefore several UTM zones. Normally, when calculating long distances like this in Australia, I would use the Geoscience Australia Lambert projection. Indeed, I began converting my data to this projection in order to begin calculating things like slope (which I also resampled to a lower resolution to match Land Use).
I'm now beginning to wonder if I am using the correct coordinate system for the route analysis. When dealing with Cost Distances, I'm assuming this type of coordinate system is appropriate. However, I'll be rasterising many polygons and I wonder if I should be using an Equal Area projection such as Australia Albers.
In short, what type of coordinate system is appropriate for performing a cost distance route analysis?