Firstly, I would like to say that while many people walk the Camino in search of solitude, in my experience most change their tune somewhat and find their fellow peregrinos one of the best parts of the experience rather than something to avoid.
That said, and with the proviso that I have only walked the Portugues from Porto, not from Lisbon, and in October rather than in the height of summer:
The
Camino Frances will give you the archetype of Camino experiences. If you read books about the Camino or watch movies, chances are that the Camino walked by the protagonists was the Frances. If you walk from the French border, you will get the familiar narrative arc (challenging pyrenees, wine region, flat endless meseta leading to the mountains of Leon/Galicia and the Cruz de Ferro, and then lush Galicia) and will see the familiar landmarks. It is the way that the vast majority of pilgrims from across Europe and the world have walked for a thousand years. There are many villages that would never have existed, and wouldn't continue to exist, without the Camino. It is built into the fabric and history of the land.
The Camino Portugues is the second most popular camino, so it is not empty and there is good infrastructure, but it is certainly not as populous as the Frances. It is definitely historical (at least the Central Route) dating back to the middle ages and was the path that Portugues royalty took to Santiago. It is significantly less strenuous than the Frances with fewer mountains, but there is more road walking and much more cobblestones.
If it were me, had I less time or wanted a gentler introduction to the Camino, I might take the Portugues as a first camino. Otherwise, I would do the Frances (between these two, I can't speak to the Norte, Primitivo, etc.). If I were only to walk one Camino, it would definitely be the Frances.
As a side note, I don't know if you intend to walk on to Finisterre/Muxia. That extension seems to me to be a much more natural extension of the Frances. There, you've been walking west for a month, towards the Atlantic, and just continue on until you get there. From the Portugues, you've been walking north the whole time and suddenly hang a left to return to the Atlantic. It might seem more natural to me to follow the Portugues with a reverse Ingles.
