We live in Taplow / Dorney too - elder daughter goes to Becky High and loves it. Younger one goes to St Pirans in Maidenhead - started in Y4. We pulled her from our catchment primary as we were concerned they were not stretching the more academic kids enough, and have not regretted the move - she is flying now.
In terms of other options this is where this area can be a challenge if they don't qualify. Personally I would not use Burnham Academy (and I did go and see it - 3 times) - it is the catchment Upper, but is most definitely an Upper. For the kids at the brighter end I think they limit their options too much. For example they only offer one lauguage - French - and many other restrictions. IMHO its better to look at the Maidenhead comprehensives if no qualification for grammar - but you should go any look yourself - it may have changed a lot since I went 2 years ago.
Altwood, Newlands (girls), and Cox Green in Maidenhead are popular comprehensives. Newlands is lovely - but not many from out of Maidenhead get in - but kids from Burnham / Taplow go to the others. There is a boys comp too - on Shoppenhangars lane - can't remember the name! Buses run along the A4 from Taplow area.
Independents - not too many choices locally cos of the grammar system - but Claires Court in Maidenhead, Licensed Victuallers in Ascot, The Abbey and Blue Coats in Reading are a few!
Good luck in your planning! It's not easy!!