A little experience. Enough to say at this point it's probably overkill, but if you start writing more geo-aware features (e.g. search nearby, overlapping course search, etc) it may save you some time vs implementing in application code.

I've used PostGIS in the past and what I can say is that I was pretty impressed with its performance. If you want to render the geometry, you could use geoserver... but make sure you have the RAM available.