Comment by bdon

Author of the OP here. I don't have a GIS background in particular; I do have a decade of experience building web mapping applications, and here's some of the foundational software I use:

http://leafletjs.com https://shapely.readthedocs.io/ https://github.com/libgeos/geos https://rasterio.readthedocs.io/ https://gdal.org http://www.angusj.com/delphi/clipper.php