GRW has it spot on for state schools. Catchment's the key for most of the grammar schools, Chesham and Burnham usually go further out - Chesham has the better results.
As for the upper schools, ie. non-selective, you'd need to compare the results with your current comps. Their levels are very respectable and improving - Amersham and Chalfont Community College would be the two to look at.
For private, Gerrards Cross has two smaller schools which cover KS3/4, St Marys for girls and Thorpe House for boys. Otherwise you're looking further afield although all have buses.
All have some degree of selection but some are more rigorous than others. Also depends if boys/girls. Berkhamsted can accommodate both although in separate schools on adjacent sites.
Otherwise for girls - Royal Masonic in Rickmansworth, Pipers Corner in Great Kingshill, the North London schools such as St Helen's and if super-academic Wycombe Abbey. Heading over towards Windsor there are other options too.
For boys the day school choice is more limited, Merchant Taylors is certainly a good option.
If you wanted to move to a nearby area with good schools look at Chorleywood - St Clement Danes is an excellent comp with a degree of selection (music and academic). Look into the South West Herts consortium for more info.
HTH!