I'm sorry, I can't help much. I don't have children so I can't tell you anything about the school situation.
I live in South Birmingham in the Frankley/Rubery area, which is fairly close to Longbridge train station. I also have friends who live in West Heath, also near Longbridge station and there is a good bus service. I have had no problems in my area, neither have my friends and there are plenty of schools around, but I have no idea how they are rated.
My one brother lives near Acock's Green Station and has had no problems where he lives, but again, there are no children so I don't know about the schools (he's actually a teacher himself, but works in Coventry
)
Solihull is good for schools (and has a train station), but the houses are more pricey than within the Birmingham boundary and I know there have been problems with some of the schools being oversubscribed as there has been a fair bit of new housing development in the area, but no new schools to go with it