Any ideas what sort of school you would want them to go to at 11+/13+? Obviously it is a while away but what would you hope for?
Ideas on this will help inform what might be best. There is a great range of schools which aren't too tricky to get into (population of kids isn't high around here and all the schools generally have space).
For example:
If you want a more public school (often 13+) then places like Amesbury, Highfield & Brookham, Aldro (boys), Edgeborough
If you want smaller nurturing then Barrow Hills feeds King Edwards now, Royal has its own juniors, St Eds goes all the way through.
If you want RGS/GHS/St Cats then St Ive's, Amesbury ...or think about going up the A3 to Lanesborough, St Cats Prep, GHS Juniors, Churcher's prep (these will be the hardest to get into and don't generally fit your 'not a hot house' criteria)
If you want to keep options open then I would go for St Ive's, Amesbury, St Hilary's, Highfield & Brookham and possibly Barrow Hills.
I personally would avoid The Royal, Longacre and St Ed's.