I live in Caversham, and the secondary schools are not in the least dreadful!
Highdown is a large comprehensive, and gets an unfair reputation locally purely because it is the local large comprehensive - so any "youth" seen doing anything slightly untoward are likely to go to Highdown. It gets very reasonable results, and has many, many children of university-educated professionals going there, if you're worried about that kind of thing. My son is in Y10 at Highdown, and doing well. (It is Ofsted rated good.)
Maiden Erlegh Chiltern Edge (MECE) is a much smaller comprehensive a bit further out. It had a troublesome time a few years back, but has turned around, and is now also rated good. I have friends with children there who are very happy with it.
A new school is opening this september, and the new head teacher has come from MECE after very successfully turning it around.
There are two grammars in Reading, Kendrick (girls) and Reading (boys).
I really enjoy living in Caversham, and if you are commuting to London it is a very good base. The station is in walking distance from central Caversham, and is on both the main Paddington line, and the Elizabeth line.