With school age children, living outside of London makes more sense, since state schools in London are a bit patchy. Of course there are superb public (i.e. private) schools in London, but if you are worried about rent budget, the additional cost may be prohibitive. The Oratory school in Knightsbridge is a good (I think free) Catholic school -- I think Tony Blair sent his kids there -- not sure if that is a good endorsement!
I don't know much about commuter villages to Paddington - others will advise. However, do note that the vast majority of UK rentals are furnished -- finding a suitable unfurnished place will limit your options. You may want to rent furnished for 6 months, and then unfurnished for 6 months, since shipping all your stuff will take a while.
Also, note that prices for commuter friendly places, although cheaper than the nice parts of London, are pricey: for 3+ bedrooms, you are looking at ~US$1M (although I haven't kept up with prices, so take with a pinch of salt).
Finally: whoever stated that Reading and London offer similar lifestyles is smoking something -- can't think of many places more soul-less than Reading.
tb