score:5
Leaving from Paris (and presumably going through Tours) is clearly not a good option given your criteria. The area around Paris and the Centre-Val-de-Loire are generally flat and the route then goes around the Massif Central, without any major mountainous area and generally less dramatic landscape. The Via Lemovicensis also includes many rather flat areas but at least it does cross the Massif Central.
So the Via Podiensis seems the best option for you, with one small caveat: Le Puy is in a relatively mountainous area and some of the steepest climbs (apart from the crossing of the Pyrenees, which is common to all three ways) would be at the very beginning (don't imagine the Rockies or even the Alps however). The rest of this route include some plateau and many hilly areas (not really mountains but not flat either) and the infrastructure is great.
Because of this, you can basically make the progression as easy as you want by stopping more frequently. Also note that the GR65 is marked all the way to Geneva. You could start somewhere east of Lyon to have a couple of days of relatively flat terrain before approaching Le Puy and the Massif Central (not sure about the infrastructure on this part of the way but finding support should not be difficult, it's not a wild area at all).
I am less familiar with the various routes in Spain but my understanding is that the Camino Frances is the only one starting in Saint-Jean-Pied-de-Port so that would be the logical option since you are apparently planning to walk one of the major French ways. It certainly boast varied landscape and great support infrastructure.