I don't think qGIS will do much for you. It is GIS software that is better suited for more advanced uses, such as working with shapefiles and raster imagery. It certainly could have its place in a map-making workflow, but since you describe yourself as a "complete newbie", iMO... it's not for you. Garmin devices are consumer products that are intended to be used with consumer-level software. qGiIS is certainly not the right software for creating and managing routes. And qGIS cannot manage Garmin maps.
On the Mac, I think Basecamp is pretty much your only option. In order to use routes, you will need a map installed on the GPS that supports routing. Almost none of the maps on this site are capable of that. Garmin City Navigator is the standard map for routing, but Garmin's 24k topo maps are also routable. Both of these options are rather expensive. To create routes, you will need the same map installed on both your computer and GPS for the best results.
Looking at your post again... it looks like you aren't quite clear on the difference between "maps" and "routes". I think you are really just interested in routes, POI's and tracks. These are considered "user data" and maps are like "system data". Basecamp is a program for managing your user data.
Basecamp does seem to be at the end of its life (although Garmin has sent some confusing signals). The current Windows version has an issue that makes it incompatible with many (if not most) of the maps on this site because it doesn't work with registry-based maps. This is not an issue with the Mac version of Basecamp, because registry-based maps were never compatible with the Mac.

Garmin is transitioning to "Garmin Explore" which is web-based software for managing its devices and your GPSMap 66 is one of the new models that support this new system. I have no experience with this, and don't have a compatible device. But that is clearly their future, so you should probably check it out. In the future, it may be all you need.