From my understanding, and gleaning from the experiences of others, I think a nice Montessori pre-school (if you have one nearby - not an option where I am, as an hour is a bit far to drive!) or agreeable conventional pre-school (have those in plentiful supply in my area) and local primary school are more than good enough before embarking on a private secondary education. We've switched to the local Catholic school for size reasons (wanted a small community and the public school is huge compared to where DS spent his first two primary years), but from my own Catholic education the main differences in education (apart from the religious component), was a uniform and relatively small fee structure.
I've got friends who attended their local primary school in the country, a nearby private high school and then went to boarding school in the city from Year 9 and that seemed to work for them.
The structure of education changes in high school, so no matter where they go it's no real advantage to have had the private primary education.
The only system I can think of that seems to benefit from the same primary education is Steiner.
Oh, and DP is very anti-religion, but hasn't fought the Catholic school thing and isn't averse to the idea of the private Catholic high school...so far...