Public school? Boarding School? Homestay?

creamsicle

For foreigners, public schools are almost as expensive as private schools so I wouldn't go for public schools unless it's a very good school.
All boarding schools are private.
I'd aim for boarding schools, ie avoid homestay. Not for Gr8.  Too young. You can't be sure of the family, the living environment, or the distance to commute to school.  
Pros for boarding schools : school matrons are professionals in taking care of children, have rules to enforce discipline in an otherwise free country, no need to travel far to school in winter, whole environment is more conducive to studying, have more friends with similar background / experience living together, food and bedroom may not be the greatest but at least there is a minimum standard to maintain.  
Cons? at Gr8, most likely have to share bedroom / bathroom with other kids.  Also, at Gr8, may not have access to a kitchenette, if there is one - not a factor if he can't cook himself.
Boarding schools are not all the same.  Some are very good academically.  Parents enroll their kids because local public schools are not good enough.  There are some other boarding schools the main selling point of which is .... boarding.  Parents don't want them to stay at home - parental problems, friends of bad influence back home, etc.  My comments above are based on the former category only.