As Kjell says, you can apply basic hillshading in ArcMap and many other packages, my personal preference is Surfer by Golden Software. In terms of interpolation/gridding, if you want a smooth looking map you can, as said, use algorithms like bilinear or minimum curvature; but if you're looking to detect features approaching the scale of your GSD, I find far better results with Kriging. If I have the resolution, even if I intend to use data in another package my workflow is to grid (Kriging) in Surfer before any visualisation, and in fact Golden Software (no connection!) have announced a beta to expose all the raster tools in Surfer directly in ArcMap, including fully-controlled Kriging (variogram control etc.).
If you're "feature hunting" from your DEM, if you haven't already done so, could I suggest you look at the free
"RVT" (Relief Visualisation Toolbox) - their Sky View Factor and open pos/neg can be quite helpful.
Dave