Use Bilinear Interpolation resampling during display
You can somewhat improve the display by changing the resampling method used from the default Nearest Neighbor to Bilinear Interpolation. Layer Properties -> Display Tab -> Resample during display using: Bilinear Interpolation.
This effect works best with DEM and the default black and white color ramp.
You will get a much better result and a lot more control over the display when using 2 raster as you have already done. Make sure you also use the Bilinear Interpolation resampling method during display.
Add DEM:
Toggle "Use Hillshade Effect" on:
Renders as follows on screen:
Change resampling during display to Bilinear Interpolation:
Since hillshade is just an overlay, you can do it anyway that gives you the desired result. However, the usual way to emphasise the terrain is to apply a vertical exaggeration. In ArcGIS you use the 'Z-factor' in the hillshade tool to do this as per the documentation here. You multiply the z conversion factor by the exageration factor. If your z-units are the same as your distance units then it will default to 1 and you can then treat it just as an exageration factor.
Best Answer
Three of the first sources that come to mind:
Or you could always download the free SRTM 30m data and create the hillshade yourself.