You could do some image processing on your base map to enhance the contours and reduce the visibility of the woodland etc. and you could attempt line tracing (using ArcScan or raster to polyline tool)to extract the features like contours and roads. However, looking at your map I'd expect either approach to give you very messy results. To be honest, I would only attempt what you want as a very last possible resort where no alternative exist, because the effort of finding good quality vector data is almost always considerably less than the effort of extracting even medium quality data from a 'busy' raster. Fortunately for you, alternatives do exist:
A quick squint at your map shows you are in New England, which is in the USA and your government make some excellent data freely available, which will give you much better contours. You can download contour tiles from the USA National Elevation Data (see Data.gov). This will look much better/clearer than trying to highlight them on your old map and you can also use the data as part of your queries as well as styling to taste in your outputs.
As for the roads and other linear features, again the USA provides TIGER Line data and you can usually get a variety of vintages to match your use-case. TIGER has been around for decades and if the linked site doesn't hold the vintage you require, it will be out there somewhere and the effort to find it will be less than the effort of trying to get decent linear features differentiated by type from any automated process on that map. Again, you will be able to style and interact with the data and the quality will be infinitely better than what can be extracted from the raster.