Upvote:6
I don't think there is anywhere with direct trains from Essex/East London to Reading? At least not until Crossrail starts.
The closest direct train you will get is from Waterloo.
See https://traintimes.org.uk/london%20waterloo/reading?changes=0
Your best option might be Egham, just off the M25 with parking at Β£7.50 per day. Though at that point you are well over halfway to Reading.
Once crossrail does open then you have a lot more options from as far East as Shenfield (1hr 42). https://www.crossrail.co.uk/route/maps/route-map
As @Muzer points out, there are fast non-stop trains from Paddington to Reading. While driving to and parking at Paddington is probably a non-starter, you could take the Hammersmith & City Line from Barking to Paddington and change trains once.