If you are looking at good state schools in the area, I would consider looking at Cirencester. Its not close to M40, but it is Cotswolds.
Woodstock North of Oxford would be closer to where you are looking for (Catchment area includes Bladon and that gorgeous house someone posted earlier!) Or the secondary school in Eynsham (Bartholomew's). Witney schools are okay too.
I would consider Newbury - Has some excellent state schools, but is along the M4 (According to AA - 57 mins commute to staines, 1 min more than from Oxford, and has much better state schools!)
Personally, a good option might well be a village inbetween Didcot and Newbury. You then have the choice of Didcot Girls' or the Downs. Easy access to Oxford, and some of the villages there are gorgeous!
Villages near Banbury (But would not recommend Banbury state schools) and the schools at Didcot (but don't even think of living there!)
Other places you've mentioned:
Faringdon - school is on the up, did have not such a good reputation for a long time, but it is improving. For 'A' levels though, consider the College at Swindon. People who I know that live there, would not necessarily recommend it, there are real areas of social depreivation there, but hidden because it is quite rural.
Chippy - Knew some teachers who taught there - they said it had a depressing atmosphere about it!
Wallingford school is not the best. Many of the students commute across to Didcot.
Avoid school catchments for Bicester and Carterton like the plague.
Hope this helps. I've taught in and around Oxford all of my teaching career, so have got a feel for the reputations of the different schools, and have met many a teacher from them on different Insets etc! I hope this helps you!