Oh yes. Many have been through this. It's the Holy Grail and prices reflect this.
As to the "how". Well, what I found worked was working out what we could afford, area-wise, size-wise; doing some checking about local school options in those areas; and then basically juggling the three criteria until i had something workable.
A lot of people choose a first home around the primary, and then move for secondary but that can be quite tricky, for various reasons. So, if school is important, it is a good idea to have secondary options in mind.
There are a lot of pretty good primaries but secondaries are a bit trickier. Perhaps you should have a look at the Good School Guide and see if any of the areas with OK secondary options are areas you can afford to move into? then choose a primary on that basis.
You could choose a first home and primary within an area on the assumption you'll have to move again - but not so far that the commute back to the primary won't be impossible for the younger ones.
(Warning: I have a cold, so I'm not sure that that makes sense.)
Where you move to is going to be dictated largely by your budget. But you know that. 